As mentioned previously, the white/carpenters glues work well on foams, as does Epoxy, foam safe CA, and Gorilla Glue. There's even a foam safe version of liquid nails at Home Depot for gluing foam insulation panels that should be compatible. With Gorilla glue, be aware of its foaming up properties and make sure the parts are taped/clamped firmly in place. The foamy squeeze out from Gorilla glue is easy to trim with a single edge razor blade afer about 1 or 2 hour when the stuff has set.

Avoid ordinary CA, and solvent based glues like Ambroid, Sigment, and Duco.