I am creating an android game out of a partner based trick taking card game. What are some generic approaches to AI players for these types of games and what are the advantages/disadvantages of each?
Implementing an AI for a trick taking game would pretty much just involve implementing the same strategy a human player would use. In this you're in luck, as trick taking game strategy has been widely covered, and I'm sure you'd be able to find a wealth of information on strategies for games like Bridge and 500.
You're helped even more by an AI's ability for perfect memory of cards played, and ability to accurately calculate card probabilities. The hard part would be coding in the subjective cues that partners use to convey their actions, such as leading a low card with the expectation of your partner trumping it.
Your best bet in my opinion would be to find a strategy which is heavy on maths and probability measuring, and use that as the basis for your AI.