As a matter of fact, there are legitimate licensing solutions--they just don't cover all the most popular games, at least not yet.
The best license management system out there, bar none, is Valve's "Steam" (
http://steampowered.com/) system. Most people are familiar with this is the basis for their internet-based software distribution model, but there is actually a special version of Steam that is available for use ("required" actually, if you're licensed) by game centers. This "cafe" version of Steam solves three problems:
(1) it does license management: you pay Valve for a certain maximum number of concurrent licenses, regardless of how many actual PCs you have, and Steam manages the licenses for you.
(2) Normal game software updates can kill your internet connection's bandwidth--World of Warcraft is the worst (but others are almost as bad): it runs a custom BitTorrent client with no bandwidth limits on every machine running the game; every time people started playing WoW in my 27-PC cafe after an update had been released, no one else in the cafe could do anything on the internet, including simple web surfing. The cafe version of Steam uses a local Steam server (which you have to provide) to fetch updates once, then disburses them to local PCs over your LAN, as needed.
(3) The cafe version of Steam lets customers save their games, automatically copying the relevent game state files onto your local Steam server. If you don't have something like this, no one can really play single-player games, since they have to start from the beginning every time they come in.
And no, Steam isn't just for games from Valve--there are lots of other publishers that are using Steam now. . . but if the game publisher doesn't have a distribution deal with Valve, Steam won't help you.
There are several other companies that are trying to do their own version of Steam specifically for game centers, but, as is often the case, these problems are actually a lot harder to solve reliably and consistently than they appear at first sight, and Valve has at least, from what I can see, a 2-year head start on everyone else trying to do this.
Could you do it yourself? A friend and I wrote all the software (
http://fun-o-matic.org/) we used my game center, and we tried to tackle license management, too, but never got beyond the early development stage with that particular module--I'm convinced there is no technical reason why it can't be done. However, as a previous poster pointed out, just because YOU think you're being fair and legal doesn't mean the game publishers will see it that way, so unless you have a special licensing agreement with every publisher, you'd be running some legal risk, anyway.