Okay, some things first, I am going to assume you have tried them:
1) When the Paladin was created, had you told the other players, including Paladinperson, that you were planning on going necromancer?
1a) Did you explicitly say that you were planning on being a 'skeleton and zombie' necromancer? If so, you don't need to do anything, you are in the right, you had the character first, you were honest.
1b) did you bring this up as soon as you knew the paladin served an undead-hating god? If so, why has this not been solved out of game, by say the paladin moving to another deity.
2) Talk to the GM and player about it, see if they are willing to ignore that part of the lore.
Alright, possible in-game ways to make it work:
1) You do not see zombies as something that should be permanent, but rather a disposable tool. A zombie is something that you animate and use for a day or two, before respectfully unanimating it and dispose of the corpse as the original owner would have wished.
2) You do not make zombies without express permission from the ex-person. They've said they have no problem with it, as long as zombies aren't strictly illegal where you are you can called the law down on the paladin if he objects.
3) Illusions, bluff, or similar.
4) Play an anti-undead necromancer or debuffer necromancer. As you want zombies/skeletons this is a last resort.
5) Get the rest of the party on your side. If all bar the paladin are fine with you making zombies then the Paladin has no support.