you have team games (doubles, triples, quadriples). where you have an ally for the entire game.
but you can also ask someone during a game to have a truce/peace agreement so that you don't attack each other for a few turns. but you can still attack each other so make sure you can trust each other.
Formal alliances are not a part of CC's game system...yet. Informal alliances that are allowed are made via game chat. Making alliances by posting on another player's wall or giving them a private message is a warnable/bannable offence.