There isn't a specific, widely recognized term for a poet of limericks. You could call them a limerick writer, limerick poet, or simply a writer of limericks.
You could also be creative and come up with your own terms, like:
* Limerickist
* Limerickian
* Limerickologist
Ultimately, the best way to describe someone who writes limericks is to simply say they write limericks! 😄