Hi,
near where I live (in australia) there's an old cemetery with graves going back to the 1880's, with old headstones etc. It's in bushland and belongs to the Methodist church. There used to be a church on the site as well but this was demolished in the 1950's. The site is on the local heritage list. I checked the legislation about heritage sites and you are guilty of an offence if you do anything that might cause the heritage value of a site to be degraded. I guess its arguable if ethically metal detecting the site would cause the heritage value to be degraded or not - this would be a matter for the courts to decide if it ever came to that. There are two very large old pine trees standing on either side of the old gate entrance and I can easily imagine in times past, children climbing and playing in those trees while they waited for their parents after Sunday sermon, so there's certainly potential for old coins etc. to be found near these trees. I was thinking of detecting outside the gates in the vicinity of the trees but havn't gotten around to it yet (outside the gates is public land) - I don't think I would detect inside the gates. By the same token though, in the last few decades the Methodist church has not spent one penny on maintaining the site and it's slowly falling into ruin.
Often cemeteries are located near where old churches used to be - so I would suggest that you not detect in the actual cemetery but do a bit of historical research (look up old parish maps etc.) to see if there were nearby any old buildings etc. associated with the cemetery, then try and detect around those old building sites if possible.
cheers,
rob