Finding a drive that would work as a second drive for backups in that system may be a challenge. It will be a bit of a job, but fitting the existing drive to a newer system using the aforementioned IDE to USB converter might still be the easiest way of doing this. The alternatives mentioned by In rerum natura might also work, but every change to a system of this vintage is going to be challenging.
I haven't checked, but is there some sort of tool that will allow you to use a USB drive to use as a backup medium? Post #17 has a link to some interesting resources.
Edit: I just remembered... there is no USB option on this system... I keep forgetting that as it is such a common interface these days!