For my daughter's first birthday, I bought packages of bath toys and split them up among the kids. I went to another party where a mom bought a bunch of books on sale, put them in a basket, and let each child choose a book as they left. I thought that was a great idea! Target often has great seasonal items in those dollar bins in the front of the store. When my second daughter turned 1, I had a Peter Rabbit theme around Easter and got little board books, little plush rabbits, and gave them to them in an inexpensive Easter basket-- we also had an egg hunt. You may be able to get inexpensive Christmas stockings & fill them with little seasonal items. A lot of the "party favor" items are choking hazards for little ones, that makes it tough. My daughter's 2nd birthday I made home made play dough and printed off coloring sheets relating to our theme and created coloring books-- more of an "art bag".
Good luck!
A.