You can try updating the Mozilla backend K-M uses or wait till next release... the 1.2b backend it uses by default is buggy with Java (gemal.dk, browserspy shows that Jave is NOT enabled). I have a guide on how to update to 1.3a release backend, on the thread Mozi-Meleon 1.3a. The upgrade fixed Java support for me and a few others, might work for you too.
Shelumi`El
Jordan
S.D.G