I was trying to make a mummy with cleric levels and the fire domain and it seems like the mummy's fire vulnerability is preventing the domain's granted fire resistance ability from displaying in PCGen. I looked in the Universal Monster Rules http://paizo.com/pathfinderRPG/prd/monsters/universalMonsterRules.html and there is nothing under the descriptions of energy resistance and vulnerability for the same type not being able to coexist within the same creature.
I've also done a search of the Paizo boards, and there's no talk of vulnerability preventing resistances (although there has been a discussion of what order they're applied in play).
Going back to 3.5, there is an official answer to the question of what order they are applied in the official FAQ (p.113 in the PDF downloadable here: https://www.wizards.com/default.asp?x=dnd/er/20030221a), confirming implicitly that a resistance and vulnerability can exist simultaneously in the same creature at least for 3.X.
It may be best to save this for a later version then. Whatever you think is best.
At revision: 22502 - 3e
At revision: 22501- 35e
At revision: 22500 - PF
All working except for grabbing a ring of energy resistance in 3.5 doesn't seem to help when there's a vulnerability (eg. a frost giant grabbing a ring of major energy resistance [fire]). I don't think the rings of elemental/energy resistance have been coded in 3.5/PF yet so I don't know if it'd be an issue for them.
At revision: 22511