The ad for Land Before Time IX said that the movie was already out, which made the earliest possible day the 10th. Then the ad for The Country Bears said that THAT movie would be out on the 17th, which narrowed it down from the 10th to the 16.

I then looked through the schedules for each of those days on the Nickstory Archives wiki, looking for the four things that aired on the day of this recording: Tiny Toons' "New Class Day" and "Toons from the Crypt", Dora's "A Present for Santa", and Spongebob's "Christmas Who". In doing so, I found them on the page for the 11th. https://nickstory.fandom.com/wiki/December_11,_2002