Some things you can do, in order of increasing difficulty:
- Get a real ISP. It might not be much more expensive to find one that gives you a static IP. I live in USWest territory; they'll give me a dynamic IP for $18 a month. csolutions.net gives me a static IP for $19 a month.
- sign up with someone like dhs.org OR
- run your own DNS server and sign up with someone like secondary.com
If you pick one of the latter options, I believe that with the DHCP protocol you're supposed to get the first chance to renew your IP when your lease expires. So if your server is always up your IP should change seldom if ever.