Well, you could use ones that are firewall-based, like 192.168.xxx.xxx or 10.1.x.x... those ones are fine because they are internal, and are based on router setups (it'd only connect people to a router on their own network).
Or, assuming we are still talking IPv4 only (I have no idea what you'd do for IPv6 as I'm totally unfamiliar with its format, though it's probably simple math), just break out the rules and use any number beyond 255. Since all IP addresses have to contain 4 numbers less than 2^8 (8 bits of 0 or 1, in case you were wondering what that root is. It's the number of combinations you can get with 8 bits), use something like 300.129.231.56.
I'd guess you probably already know that based on your initial question, so if that's the case, I'd use a firewall-reserved one like 192.168.x.x or 10.1.x.x. There probably are other reserved ones, I just don't know them.