The One In Barbados, part 1 - S9-E23
Trivia: When Joey and Rachel are looking for nametags to con their way into the convention, the name picked out for Rachel is Kate Miller. I just found it a bit odd that not a flicker of recognition passes across Joey's face, considering that was the name of Dina Meyer's character from a few seasons back who he was in love with.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.