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Your question is "is it legal ....?". The answer is probably yes. This would be because of a combination of factors:
a) public access is allowed (ie.: there's nothing to stop or prohibit you from meandering about, being there in the first place, etc...).
b) Sure, the permission to pass is no-doubt "revokable by owner" (much like a shopping center or whatever).
c) barring an rules by that owner saying that you can't do such & such, then ... I suppose that technically, they'd have to appraise you of such a thing. Because I mean, they can't say it is "trespassing", since the graveyard is open to the public.
BUT!! this isn't to say that they might not call the police, and try to say you were "vandalizing" or "destroying" or something like that, which WOULD run afoul of existing laws. Now of course you and I know that metal detecting is not "vandalizing" or "destroying" (because you'll leave no trace of your presence). But just saying that anyone can level such accusations, and you're going to be "hard-pressed" to disprove it, d/t the ...... uh ...... image of someone "detecting in a graveyard".
So your question of "is it legal", is probably yes, but is it wise? Is probably no. It just carries too much connotations, sensitivities, etc... Even though you know graves are 6 ft. deep, and you are only looking for coins a few inches, yet there are some observers who are superstitious, etc.... given the location.