@xyphoid
Since MorphOS is AmigaOS Classic compatible, you could try some of the software for Classic AmigaOS. Another solution could be to use another computer to get online, and connect via LAN (as Piru suggested), or use a router (or network hub) that supports dial-up.
If you have a spare PC that you don't need (could be the oldest box in town), you could install Linux or BSD on it, and configure it as a DHCP server. You could set up scripts to automatically dial your modem into the internet, and automatically terminate the connection (there are some tutorials for that AFAIK) when the connection is idle for a specified time. If that works, you'd simply buy a small network hub and connect all your boxes to it, including your "new" DHCP server. Then, you simply set up the remaining boxes as DHCP clients (i.e. in the TCP/IP configuration, specify "get TCP/IP address and DNS address from a DHCP server"). And you're all done, you'll never need to worry about it anymore. But it is a bit of work!
[ Edited by voyager2007 on 2008/7/12 22:37 ]