I am wanting to buy 36 acres of land. The only way to access the land is from an old coal mine road which I would not own. Are there laws that would allow me an easement to use the road if the roads owner is not willing to allow me access?

This may vary, from "nation to nation" you did not mentino if you are in Germany or France. Perhaps the USA or Mexico.

If you are in certain nations all you need to do is bribe the right government people ( or pehaps in any nation after watching the news today)

But you need to first see if this is an official road or merely a road used.
You will have to get an easment for the property from the property owners, normally done by payment of funds for this purpose and promise of upkeep of the road. Or exchange of a some ajouring property for the road.

If it has been used as a public road for a certain amount of times, there are times you can get it declared open by the courts, but the last few cases I have seen like that have been turned down ( but in these cases there were other roads available also)

Since the laws in your area vary, I will assume you are using an attorney for your propery purchase and a real estate agent to represent you.
Both should know the laws for your area. Any offer for this property should include a clause for the agreemetn on this road.