In the order ranking from the quickest:
1. Daily mission. Daily mission is unlocked at level 3 and usually reward in the thousands.
2. Accept friend's heart request within an hour, which will give you 200 coins.
3. Inviting friend gets you 500 coins, although depending on your friend list there may be a limited number of friend you can invite.
4. Play the game. Each game will give you coins depending on how many tsum you clear.