Unfortunately, the only way to guarantee your address won't overlap with something else is to purchase a block of routable public IP address space.
Having said that you could try finding parts of the RFC 1918 address space that are less popular. For example, 192.168.x address space is commonly used in residential and small business networks, possibly because it's the default on so many low end network devices. I'd guess though that at least 90% of the time people using 192.168.x address space are using it in class C sized blocks and usually are starting their subnet addressing at 192.168.0.x. You are probably a lot less likely to find people using 192.168.255.x, so that might be a good choice.
The 10.x.x.x space is also commonly used, most big enterprise internal networks I've seen are 10.x space. But I've seldom seen people using the 172.16-31.x space. I'd be willing to bet you'd very rarely find someone already using 172.31.255.x for example.
And finally, if you are going to use non-RFC1918 space, at least try to find space that doesn't belong to someone else and isn't likely to be allocated for public usage anytime in the future. There's an interesting article here at etherealmind.com where the author is talking about using the RFC 3330 192.18.x address space that's reserved for benchmark tests. That would probably be workable for your VPN example, unless of course one of your VPN users works for a company the makes or benchmarks network equipment. :-)