Does it have a tuneable head (some sort of adjusting screws inside, outside or inside the frame)? Do you know who the maker is? Is the drumhead have a piece of skin, a piece of tanned leather, or synthetic?

A few details on the bodhran particulars will help get you more personalized advice. ;)

For instance, I have a bodhran made by Fred Halpin from Gloucester, Ontario. The head is actually a fairly thick piece of tanned leather and there is a patented system for tuning it made up of several set-screws adjusted with an Allen wrench connected to threaded shafts inside the frame itself. This bodhran produces a very deep boomy sound but is limited in the sorts of voices I can get out of it. But it suits my purposes for the use I put it too. I also have a synthetic skin one which is fairly rugged, cheap, and loud; it too is limited in it's voicing, but I can play the damn thing in a rainstorm and it won't change pitch. I also have a regular goatskin bodhran, but it's always been picky to deal with, since I often lay it aside for several songs then pick it up later; besides, the damn thing ripped at the frame. I have to replace the skin someday.

A design painted or drawn on the skin with a marker won't change the sound typically, but is likely to wear off with use.