This may sound like a strange request, so let me introduce myself: My name is (Your Name) and I have lived in (Name of Town) for (Length of Time). I am (Your Age) years old, married with four children. Normally I would prefer to approach you in person, however I feel that a letter before hand is a better emissary than just knocking on your door at an inconvenient time and invading your privacy.
I have been engaged in the hobby of metal detecting for (your number of years) and find it a healthful, enjoyable pastime that allows me to meet many interesting people. The thrill of finding old coins, buttons, etc. is very exciting to me.
Recently, I have researched information that your property and the area surrounding it goes back many years. I would like to obtain permission for myself and a friend to detect your property.
I want you to understand that I always respect the property that I search and try to leave it in the same condition that I found it. Normally the targets are no deeper than 4 or 5 inches and I retrieve them such that the ground appears not to be disturbed.
In addition, I would like to offer my services to you. Perhaps you or someone you know has lost a valuable ring, a cache or a farm tool. I would be willing to assist just for the thrill of the search.
I have enclosed a self addressed envelope for your convenience and would be happy to meet with you if further discussion is required.