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Throughout Game of Thrones Tyrion attempts to tell a joke about walking into a brothel with honeycomb and a jackass but never gets to finish it. I know of a similar joke but wondered if there is a canonical answer/punchline to his joke?

As far as I know Tyrion only tries to tell the joke twice and both times is interrupted almost as soon as he begins. In season 1 episode 6, "A Golden Crown", at his trial he barely gets the opening line out of the way:

Tyrion: I once brought a jackass and a honeycomb into a brothel...

Much later on in season 6 episode 8, "No One", he doesn't get much further:

Tyrion: I once walked into a brothel with a honeycomb and a jackass. The madam says...

So, the answer to is there a canonical answer is no. If you want some possibilities of what it could be I know of a few; here are a couple from this reddit thread.

Tyrion walks into a brothel with a honeycomb and a jackass.

Madame: What can we do for you?

Tyrion: I need a woman to lay with, for mine has left me.

Madame: Whatever for? And what's with the honeycomb and the mule?

Tyrion: My woman found a genie in a bottle, and he granted her three wishes. The first was for a house fit for a queen, so he gave her this damn honeycomb. The second wish was that she have the nicest ass in all the land, so he gave her this damn donkey...

Madame: And what about the third wish?

Tyrion: Well... she asked the genie to make my cock hang down past my knee.

Madame: Well that one's not so bad eh?

Tyrion: Not so bad!? I used to be six foot three!

I once took a honeycomb and a jackass into a brothel, and the madam asked me what I wanted. I said I would like to trade the honeycomb for a meal, and the jackass for a night with the most beautiful woman.

She asked me why I did not simply eat the honeycomb. I said the same reason I want to trade the jackass, I'm tired of having the same thing every night.