I think my former shop did it as well as anywhere I've been.
There was a 3-ring binder with 12 monthly calendar pages in it. No one but the boss wrote anything in it, and when people gave him time off requests, he wrote them in the binder to make it official. Once 2 people were taking that week (full or more than 2-3 days), it was "locked" and no one else could take PTO during that week. The binder was kept in a specific spot on his desk that everyone had access to, and was at his fingertips when he was putting together schedules.
As far as requesting time off, it went on a rotating thing based on rank and seniority. Starting with the boss and his assistants, then progressing through rank, people could request PTO time, 2 weeks (or 10 days) at a time. When it got to the bottom, it went back up to the top for 2 more weeks of requests, and so on until everyone had all their PTO time scheduled or said "Skip me, I'll schedule it later." That way the bosses and people with most seniority got the first pick, but couldn't take all the best weeks and leave the newest people with last choice of vacation time. And with it being so cut-and-dried, there was minimal bitching about wanting to take vacation time and having the request be denied. The boss put a checklist in the front inside folder of the binder that had the PTO policy, the listing of the selection order and how many weeks every employee had coming.
On the holidays, there was no one allowed to take vacation during holiday weeks. The thinking was that with things being as short-staffed as it was toward the end, if anyone took off for the week of Christmas, for example, pretty much the rest of the desk would have to work 5 days that week and no one else would get a holiday day off somewhere in there. I didn't necessarily agree with that part of it, but I saw why it was done.