If permission was given with no expectation of you giving the finds to the property owner you should keep it to yourself, gold makes people change. I guess it is according to what your conscience tells you to do but I see no obligation if there were no expectations that you would show or give the property owner the finds.
Gold does funny things to people, or not so funny things. I wouldn't say anything about a gold coin. If the owner told me that such and such might be buried on the property and I found it then I might feel an obligation to split it, but i'd split it my way. If possible, i'd remove it, value it, and split it by value, probably 60/40... then negotiate to 50/50 if they complained, or I might keep it... according to the situation and according to what was said.
One gold coin... nah. I'd keep it, why cause trouble and possible hard feelings over one coin. Besides, you spent good money on a detector, took the time to learn it, put in lots of hours, asked permission, got permission, and found something good... it is the fruit of your labor... You had permission to hunt, if they thought that you were looking for nails and pulltabs then I don't know what to say. They, on some level, had to know that you might find something of value, yet they gave you permission to hunt. It is yours. Honestly, if they don't care that you dig and keep a nickel they shouldn't care that you dig and keep a gold coin... yet the heart of man is.. well, you know how it is, it is deceitful. Don't stir it up.
So... don't make trouble where there is none... unless you really believe that you have a moral oblgation to tell them, then you take your chances, but you should give it some thought until you are sure of your reasonings.
Julien