How to buy a portion of your neighbor’s property .?

How to buy a portion of your neighbor’s property .
Between my property and my neighbor’s is a drop down area that is not useable for them I guess it would be considered a tear drop landscape. I have had my property surveyed and I know where my property line ends. I would like to take out a tree line and have it landscaped, for this to look right I would have to do some work on neighbor’s property due to the configuration of the land. We have already agreed to build a fence and go half of the cost of having someone come in and take care of some trees. If I proposed a deal with them asking to purchase of the land would this be costly if only a 2 ft in depth for a length of 77 ft were to be purchased. I don’t want to spend all the money to have a fence and landscaping done if only they sale the property, and I would have to fight it out with the new owners that would want to reclaim the property that belonged to them. What paper work would I have to do? Could I trade them the cost of the fence and their trees to removed and landscaping to done for the property line to be extended if both of use owned about .17 or acre. I like my neighbors and I don’t want to burn bridges, how should I go about my proposal.

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