As far as I know Tyrion only tries to tell the joke thrice and each time 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...
Lastly, in Season 8 Episode 6, "The Iron Throne", the scene ends with him starting it.
Tyrion: I once brought a jackass and a honeycomb into a brothel.
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.