Be warned that a lot of them know that some people will pay to hunt their land. Be prepared to be asked for money especially if he's been asked before. You might end up having to pay if the property has very good deer. It's simple economics and these people expect their land to make money.
If you don't want to pay then be prepared to ask a lot of people. If one says no then ask if he knows of another farmer who has a deer problem on his property. Go to that farmer and say, "Bob down the road refered me to you about the deer that have been giving you a problem, I'm a hunter and could realy help you clear them out." In his mind, you know his neighbor Bob and Bob think well enough of you to send you to him. You must be an okay guy.
Let them know that you will be safe and won't shoot around the livestock and will always close any gates. Give them every courtesy you'd want a stranger to give your own mother and you might end up with permission to hunt more properties than just his own.