I didn't have a rainbow, any trees, I whack pinatas,seedos,sprinkling,sours,and wild pinatas a WHOLE lot. And yet still a jeli came to my garden. All i had to do was give him a whack and he was mine! You don't need any of the requirements above to get a Jeli! My full story is: i waited for him to be still, then i quickly placed fencing around him thinking it was how to "capture it". When nothing happened i got frustrated and whacked him with my shovel and...POOF...he was a resident!

WARNING:this might have been a glitch in my game but I highly doubt it.