Starting from any distro you like...
1. Does your BIOS allow booting from USB devices? If so maybe you can just do a standard installation on the USB drive and set it as first boot device.
2. Do you have a floppy drive? Most installation methods give the option of making a boot floppy.
3. You may be able to install to the USB drive and then reboot using the installation CD by giving the right kernel parameters at the boot prompt.
4. Failing all this, you can install to the USB drive and make your own boot CD using e.g. the isolinux boot loader:
I'm not familiar with this myself - I guess it needs a bit of technical know-how to set up. Isolinux is a variant of syslinux, the standard bootloader for boot floppies.