I don't know what kind of plastic your part is but there is a two part
plastic cement that bonds well to many of the plastics that are hard
to glue. I don't remember the name

Ive had great success mending most plastics of all kinds (varying degrees
with poly-types) using Devcon Plastic Welder:

http://www.amazon.com/Devcon-22045-P.../dp/B003NUGL9S

Its my go-to solution when fixing anything plastic.

Cool phone. Brings back memories. Ours was (at different times, replacements
installed after family of 6 abused it) red, yellow, black, white. With
extra-long handset cord, of course.

Good luck.