Patti's recommendation of fluorescent poster board is a good one. My son was working on a science fair project earlier in the school year that featured black light fluorescence as a primary component. We bought several bottles of fluorescent paint only to discover that it wouldn't cover paper or cardboard effectively at all. We ended up picking up some fluorescent poster board for just 25¢ or 35¢ a sheet, and figured out how to cut it into the shapes we needed, sticking it onto the backing with double-sided tape. It turned out great - he won a ribbon and got an A on the project.
This might not be what you had in mind, but there's a style of "flat" puppet that's like a sign on a stick, cut out in the shape of different characters. If you want to be tricky you can put a different character on each side of the puppet "sign." You could even have the same character on both sides of the puppet, but on one side it's smiling and on the other side it's frowning, or surprised, or scared, or whatever the story calls for. Then just flip the puppet around to make it go from laughing to crying, or change from one character to another, depending on the story.
Some puppets like this even have moving parts which can be controlled with rods, or using a cord like those old-fashioned jumping jack style puppets. If all of the parts of the faces, limbs, and clothing are made of pieces of different colored fluorescent poster board assembled together it will look great under black light - though you will be limited to the colors of fluorescent poster board available to you.
I think that Patti mentioned making characters like butterflies or flowers as likely candidates for poster board puppets or props - colorful tropical birds or fish might be fun as well. Remember too that you can just use the poster board as a covering, and not as the structural base. Maybe use some heavier pasteboard or corrugated cardboard and attach that to the stick first, and then cover it with your pieces of fluorescent poster board using glue or double-sided tape, (there is also fluorescent paper available which can be used instead of the poster board).
Depending on the age, strength, and skill of your puppeteers you can make the flat puppets larger or smaller, even building two or three-person puppets - if you want very large characters, or ones with complicated moving parts. You could also make very small puppets, using popsicle sticks, tongue depressors, or wooden paint stirring sticks as handles, and hand them out to kids in the audience after the show.
I don't have any photos or links handy to show you the kind of flat puppets on-a-stick that I mean, but if you're having trouble visualizing them - think of paper dolls on a stick, but on a larger scale. The only drawback is that if you try to use non-fluorescent materials to color them, then under black light the non-fluorescent materials will just look like dark splotches. Fluorescent poster board can also be rolled into cylinders or used to cover the sides of cardboard boxes or simple styrofoam shapes, if you want to make something more three dimensional.
I hope this helps, at least until you can find or make "real" black light puppets.

Ron G.
PS
Here's a link to a page on MarthaStewart.com which shows how to make a colorful, flat paper dragon stick puppet, which is hinged so it can wiggle and dance. That might translate well into a fluorescent caterpillar puppet to go with a butterfly puppet...
http://marthastewart.com/portal/site/mslo/menuitem/dragon_puppetPPS
After we'd already completed the science fair project using fluorescent poster board we discovered that our local Hobby Lobby carried the Createx fluorescent paint sets on the air brush aisle. You could check there, if you have one nearby. I've also seen those paints for sale on eBay.