You can play some matches all the times you want, just talking to one of these people:

1) Veteran (ふるかぶ Furukabu): location. You unlock his friendly matches during the 2nd chapter.
You can play vs IE1 teams and IE2 team: IE2 teams are unlocked during the story, for IE1 teams you have to talk to their captains in a certain order (excluding Umbrella, Inazuma Kids and Street Sally's). Here's a list.
Occult: Talisman is in the 1st screen of Nara, in front of the stairs (screenshot).
Wild: Chicken is at the deer park, to the right of the statue (screenshot).
Brainwashing: Feldt is at the Northern Ridge in Hokkaido (screenshot).
Umbrella: Edmonds is at his school (screenshot).
Inazuma KFC: Maddie is near the soccer field at the river bank (screenshot).
Street Sally's: Samantha is waiting for you at the soccer field in the shopping area (screenshot).
Otaku: Talk to Idol at the maid café (screenshot).
Royal Academy: Talk to Drent at Royal Academy Gate (screenshot).
Shuriken: Cloak is at the entrance of Kyoto (screenshot).
Farm: Greeny is at Fukuoka, near the empty lot (screenshot).
Kirkwood: Murdock bros are at the entrance of Fuji forest (screenshot).
Zeus: You'll eventually unlock it during the story (9th chapter).

2) Mary Times coach: location. To unlock his tournament beat Dark Emperors at least once.

3) Alpine coach: location. To unlock his tournament beat Dark Emperors at least twice.

4) Suzette's mama: location. Win with S rank 3 matches of Mary Times coach and 3 of Alpine.

5) Otaku coach: location. Download the key of the shopping area warehouse via wi-fi.



Veteran


1: Street Sally's (一番街 Ichibangai)
2: Inazuma KFC (稲妻KFC)
3: Umbrella (傘美野 Kasamino)
4: Gemini Storm (ジェミニストーム)
5: Wild (野生 Nose)
6: Occult (尾刈斗)
7: Secret Service (SPフィクサーズ SP Fixers)
8: Brainwashing (御影専農 Mikage Sennou)
9: Otaku (秋葉名戸 Shuuyou Meito)
10: Royal Academy (帝国学園 Teikoku Gakuen)
11: Shuriken (戦国伊賀島 Sengoku Igajima)

Chest A
Normal rank: Fine Veggies (ごくじょうのおでん Gokujou no oden)
S rank: Big Moves! (ちょうわざ! Chouwaza!)




12: Royal Academy Redux (真・帝国学園 Shin Teikoku Gakuen)
13: Epsilon (イプシロン)
14: Advanced Epsilon (イプシロン改 Epsilon Kai)
15: Genesis (ザ・ジェネシス)
16: Alpine (白恋 Hakuren)
17: Cloister Divinity (漫遊寺 Manyuuji)
18: Triple C (大阪ギャルズ Osaka Gals)
19: Fauxshore (陽花戸 Yokato)
20: Mary Times Memorial (大海原 Oumihara)
21: Farm (千羽山 Senbayama)
22: Kirkwood (木戸川 Kidokawa)
23: Zeus (世宇子)

Chest B
Normal rank: Tsunami Boost (ツナミブースト)
S rank: Economy! (セツヤク! Setsuyaku!)

Chest C
Normal rank: Old Pin Badge (古びたピンバッチ)
S rank: Big Moves! (ちょうわざ! Chouwaza!)

Chest D
Normal rank: Inazuma Bracelet (イナズマミサンガ Inazuma miçanga) [Guts + 10]
S rank: Wyvern Crash (ワイバーンクラッシュ)



Mary Times Coach


1: Neo Royal (ネオ帝国 Neo Teikoku) [drop: Power Element]
2: Masked Men B (マスクマンB) - You can use only players with level ≤ 50 (or 35 if you play the jap version) - [drop: Keeper Plus]
3 FIRESTORM: Team Canon (チーム・カノン) [drop: Speed Plus]
3 BLIZZARD: Team Syon (チーム・マサト Team Masato) [drop: Critical!]
4: Alius A (エイリアA Aliea A) [drop: Shoot Plus]
5: Robot Guards (警備マシンズ) [drop: Move It!]
6 FIRESTORM: Prominence (プロミネンス)
6 BLIZZARD: Diamond Dust (ダイヤモンドダスト)
7: Chaos (ザ・カオス) [drop: Everyone Move It!]
8: Front & Back Kings A (表と裏の王者A Omote to Ura no Ouja A) [drop: Charm Up!]
9: Advanced Occult (オカルト改 Occult Kai)
10: Little Team (リトルチーム) - You can use only players with level ≤ 50 - [drop: Cool Up!]
11: Team Inazuma A (チーム・イナズマA)

Chest A
Normal rank: Study (がくしゅう Gakushuu)
S rank: Wyvern Blizzard (ワイバーンブリザード)




12: Benchers 1 (ベンチーズ1) [drop: Keeper Plus]
13: The Card (ザ・カード) - You can use air players only
14: Raimon Subs A (ウラ・ライモンA Ura Raimon A) [drop: Shot Force]
15: Gods And Aliens (神と宇宙 Kami to Uchuu) [drop: Study]
16: Old Kirkwood (オールド木戸川 Old Kidokawa) [drop: Economy!]
17: FF Regional Pick B (FF地区選抜B FF Chiku Senbatsu B) - You can use only players with level ≤ 50 - [drop: Big Moves!]
18: Benchers 2 (ベンチーズ2) [drop: Charm Up!]
19: Inazuma 08 (イナズマ'08 Inazuma '08) [drop: Recovery]

Chest B
FIRESTORM Normal rank: Canon Evans (円堂カノン Endou Canon)
BLIZZARD Normal rank: Syon Blaze (豪炎寺真人 Gouenji Masato)
S rank: Nathan Swift (風丸一郎太 Kazemaru Ichirouta)

Chest C
Normal rank: Whale Guard (ホエールガード)
S rank: Steve Grim (半田真一 Handa Shinichi)



Alpine Coach


1: Dark's All Stars (影山オールスター Kageyama All Stars) [drop: Slack Off]
2: Advanced Secret Service (SP改 SP Kai) [drop: Economy!]
3: Benchers 3 (ベンチーズ3)
4: Alius B (エイリアB Aliea B) [drop: Shoot Plus]
5: Front & Back Kings B (表と裏の王者B Omote to Ura no Ouja B)
6: Advanced Kids (稲妻KFC改 Inazuma KFC Kai)
7: Glasses A (○メガネ○A OMeganeO A) - You can use only players who don't know catch techniques - [drop: Jinx]
8: Foreign Students (留学チーム Ryuugaku Team) - You can use only players who don't know shot techniques (trick: you can use Scott and Dvalin and then change their alter-ego) - [drop: Speed Force]




9: Cutesy A (キャッピキャピA Kyappi kyapi A) - You can't use girls - [drop: No Element]
10: National Team B (全国チーム選抜B Zenkoku Team Senbatsu B) - [drop: Offence Plus]
11: Grown-Ups (アダルトチーム Adult Team) [drop: Defence Plus]
12: National Youth A (全日本ユースA Zennihon Youth A) [drop: Lucky!]
13: Benchers 4 (ベンチーズ4)
14: Raimon Subs B (ウラ・ライモンB Ura Raimon B) [drop: Shot Force]
15: FF National Pick B (FF全国選抜B FF Zenkoku Senbatsu B) [drop: Power Element]
16: Inazuma 09 (イナズマ'09 Inazuma '09) [drop: Recovery]

Chest A
Normal rank: The Tower (ザ・タワー)
S rank: Celia Hills (音無春奈 Otonashi Haruna)

Chest B
Normal rank: Whirlwind Force (せんぷうじん Senpuujin)
S rank: Jim Wraith (影野仁 Kageno Jin)



Suzette's mama


1: Masked Men A (マスクマンA) - You can use only players with level ≤ 50 (or 35 if you play the jap version) - [drop: Charm Up!]
2: Super Triple C (スーパー大阪CCC Super Osaka CCC) [drop: Defence Force]
3: Strange Guys B (あやしいやつらB Ayashii yatsura B)
4: Benchers 5 (ベンチーズ5) [drop: Cool Up!]
5: New Alpine (NEW白恋 NEW Hakuren) - In the jap version you can play this match with 2 DS only
6: New Cloister (NEW漫遊寺 NEW Manyuuji) - In the jap version you can play this match with 2 DS only - [drop: Recovery]
7: New Fauxshore (NEW陽花戸 NEW Yokato) - In the jap version you can play this match with 2 DS only - [drop: Power Element]
8: New Mary Times (NEW大海原 NEW Oumihara) - In the jap version you can play this match with 2 DS only




9: National Team A (全国チーム選抜A Zenkoku Team Senbatsu A)
10: FF Regional Pick A (FF地区選抜A FF Chiku Senbatsu A) [drop: Big Moves!]
11: FF National Pick A (FF地全国選抜A FF Zenkoku Senbatsu A) - You can use only players with level ≤ 50
12: National Youth B (全日本ユースB Zennihon Youth B) [drop: Shoot Plus]
13: New Royal Redux (NEW真・帝国 NEW Shin Teikoku) - In the jap version you can play this match with 2 DS only - [drop: Charm Up!] or Big Moves!]
14: New Gemini (NEWジェミニ NEW Gemini) - In the jap version you can play this match with 2 DS only - [drop: Big Moves!]
15: New Epsilon (NEWイプシロン NEW Epsilon) - In the jap version you can play this match with 2 DS only - [drop: Slack Off]
16: New Genesis (NEWジェネシス NEW Genesis) - In the jap version you can play this match with 2 DS only - [drop: Study]

Chest A
Normal rank: Steeple Shot (つうてんかくシュート Tsuutenkaku Shoot)
S rank: Sam Kincaid (宍戸佐吉 Shishido Sakichi)

Chest B
Normal rank: Maize Boots (メイズスパイク Maize Spike) [Shoot + 12, FP + 5 and TP + 5]
S rank: Death Zone 2 (デスゾーン2)



Otaku Coach


1: Inazuma Veterans (雷門OB Raimon OB) [drop: Lucky!]
2: Super Otaku (スーパー秋葉名戸 Super Shuuyou Meito) [drop: Offence Force]
3: Glasses B (○メガネ○B OMeganeO B) - You can use only players who don't know catch techniques
4: Strange Guys A (あやしいやつらA Ayashii yatsura A)
5: New Wild (NEW野生 NEW Nose) - In the jap version you can play this match with 2 DS only - [drop: Defence Force]
6: New Brainwashing (NEW御影専農 NEW Mikage Sennou) - In the jap version you can play this match with 2 DS only - [drop: Recovery]
7: New Otaku (NEW秋葉名戸 NEW Shuuyou Meito) - In the jap version you can play this match with 2 DS only - [drop: Big Moves!]
8: New Royal Academy (NEW帝国 NEW Teikoku) - In the jap version you can play this match with 2 DS only - [drop: Speed Force]




9: Cutesy B (キャッピキャピB Kyappi kyapi B) - You can't use girls
10: Benchers 6 (ベンチーズ6) [drop: No Element]
11: Team Inazuma B (チーム・イナズマB) [drop: Power Element]
12: Young Inazuma (ヤングイナズマ) [drop: Trickery!]
13: New Shuriken (NEW戦国伊賀島 NEW Sengoku Igajima) - In the jap version you can play this match with 2 DS only - [drop: Defence Plus]
14: New Farm (NEW千羽山 NEW Senbayama) - In the jap version you can play this match with 2 DS only - [drop: Shot Force]
15: New Kirkwood (NEW木戸川清修 NEW Kidokawa Seishuu) - In the jap version you can play this match with 2 DS only - [drop: Economy!]
16: New Zeus (NEW世宇子 NEW Zeus) - In the jap version you can play this match with 2 DS only - [drop: Trickery!]

Chest A
Normal rank: Stone Wall (ロックウォールダム Rockwall Dam)
S rank: Perfect Tower (パーフェクト・タワー)

Chest B
Normal rank: Emperor Penguin No.1 (こうていペンギン1ごう Kōtei Penguin 1-gō)
S rank: Maxwell "Max" Carson (松野空介 Matsuno "Max" Kuusuke)