There many Amsats with Packet "Repeaters" and/or Packet BBS systems, including the ISS.
You need software to tell you when they are in range. Some are 38.4K bps.
Orbitron and similar packages need updates every few weeks, but this only takes a few minutes even on a poor dialup system. If there is demand the files could be available on BBS and packet FTP for users with Packet but no Internet.
The satellite infoemation files or TLEs cover every man made object in orbit, not just the Amsats!