(A discussion in the Yahoo! FZ10 forum)
Some people use plastic ties, others use a piece of string, or nothing at all.
Aquarium rubber caulking should not require a solvent to be removed (Janis Whitcomb), nor should rubber cement (Eric) from an art supply store.
Silicone glue should be used sparingly, perhaps applied with a toothpick (Strat), and may require a strong solvent to be removed (Billy).
{Picture below `Fording Ford'. Taken by Stratis and computer manipulated.}
Others prefer to modify the eyepiece of the FZ10 so that the rubber eyecup does not fall off so easily (dpreview thread by Reid Bridges and ferness 261, commencing 21 December 2004).