Yep, can do, I've done a few now (only had the player about a week).
First part is to actually obtain the flv (flash video) from youtube. You need a third-party plugin to do this, in Firefox there are quite a few, such as "UnPlug" and "Video Downloader". Just wait for the video to fully load, click the button for the plugin (most put a button on your toolbar or status bar), and save as a *.flv file.
Then get
MediaCoder, a FREE transcoder that can convert all sorts of formats to and from each other. Output as an avi, and fiddle with the size settings to get an aspect ratio that fits your needs: eg., my chipod uses 128x128, so I just add some space to the top and bottom of the usual 3:4 ratio videos (eg 320x240) to make them 1:1 (320x320). Sorry if that's unclear, I'm at work and a bit rushed.
ops:
Anyway, then convert your avi to amv with the amv convert tool.
So: get the flv, convert it to avi, change it's aspect ratio to suit your screen (amv converter will resize to the right size), then convert to amv. Once you've done this a few times, you can make default settings so you just need to load the file and hit "transcode".