If Tiger wasn't able to install on your iBook, then it could be because you might be using an OEM disc. These are usually solid gray and only work with the Mac models that they ship with. You need the retail version of Tiger, which has a silver "X" on top of a black background in the retail version (both upgrade and full installations).
From the specs given, you could even install Leopard on that iBook but I don't know how snappy it would be compared to Tiger. Tiger should install just fine on that system, but not from an OEM disc that was from another Mac that wasn't an iBook of that revision.
• Apple iMac G5 17" (2 GHz G5) - Mac OS X 10.5.8/Ubuntu 10.04
• Asus Eee PC 901 (1.6 GHz Atom N270) - Fedora 13
• Apple Macintosh Quadra 650 (33 MHz MC68040) - Mac OS 8.1
• "JHVH-1" (2 GHz AMD Athlon XP 2400+) - Slackware 13.1