Question tag

Perhaps you'd be willing to give it a try first.

I enjoyed the opera. Didn't you?

I'm going to take a shower. Aren't you?

I'll bet she's going to win the contest. Won't you?


I could really go for a cold beer. Couldn't you?

The trick in your example is to figure out what the contraction "I'd" really stands for!

I think the answer is : wouldn't I?

Aha! You're very close! I think that usage is rather British.
I really fixed him, didn't I? I'd like to go out with her, wouldn't I?
I guess you could call it a rhetorical question.

I believe in this case, we're extending an invitation to another person:
I'd like to play tennis. Wouldn't you?
It's similar to: I'd like to go out

Is this a question you invented, or did you take it from a textbook? If the latter, I think it's a poor question. It seems to be asking for "I'd like to play tennis, wouldn't I?", but that's an unusual thing to say, making one uncertain if it really is the expected answer.