Tricky upgrade question

Here’s a tricky chicken-and-egg question for Mac admin types...

I have—actually, a relative of mine has—an iMac running Mac OS 9.0.4 that I’d like to upgrade to OS X.

The CD-ROM drive is broken, so the idea is to buy an external CD drive and hook it up. But all the CD drives we can find require OS 9.1 or greater.

Is there another way to install OS X on this machine? Or a way to install 9.1 so we can get a CD drive running so we can install OS X?