There are 3 types of coaches in the game: Common Coach, Rare Coach, and Epic Coach.
Common Coach is the default coach owned at the beginning of the game. A maximum of 12 contracts can be received on Common Coach and these contracts are renewed hourly.
When you reach a certain number of fans, Rare Coach and Epic Coach are unlocked.
Rare Coach and Epic Coach have 5 contracts when they are unlocked, and more contracts can be obtained with diamonds. Contracts may also come out of chests. There is no contract limit for Rare Coach and Epic Coach.
Common Coach has 2, Rare Coach has 3, and Epic Coach has 4 players.