I think it's simple and there are a few ways that I have been successfull.

Knock on 10 doors and you will get at least one place to hunt. I really think you will get 2. Look presentable and be polite.

Always start with Bowhunting... Don't bring up firearm season untill you get to know the landowners a little better. If they don't really mind they will offer it to you.

ALWAYS.... Carry a fill in the blank permission slip in your vehical. You never know when you might meet a person at a party or a social eventof a friend of a friend or whatever that is complaining about the deer. They will most likely sign it right away.