What you can do is give every database it's own dbspaces. The backup and restore tools from Informix work on the dbspace level.
There are some issues you need to be aware of:
1. Backup's made with onbar without the -w option are able to restore a single or multiple but REQUIRE logical logs backup to restore (anaything).
2. Backups with the -w option only allow full restores
So if you make logical log backup's then you can restore a specific database (if placed in separate dbspace) without taking the other ones offline. Beware there is another but. You cannot do a poit-in-time restore of not all dbspaces. So you can restore a database, but it must be done up to the crash (if it was a physical problem) or with all logical logs (if it was a logical problem). With Informix technology it is not possible yet to recover for example a database that has a dropped table. Choices in this case are: a) go with the whole instance back to a point before the drop or b) recover the dbspaces and the drop (in this case the restore is actually useless).
In IDS 9.50 (which will be coming out in 2005 Q1) probably a table level restore is possible.