I don't think any store here in Toronto even has lay away. I know our Wal-Mart used to have it but stopped at the same time as yours.
I know this is going to seem obvious, but when I was in college and wanted to get gifts for friends and family, I used the cash stash system. I would put all my change (mostly loonies, toonies and quarters) into an old peanut butter jar and make a vow not to touch it. Then on the 15th of October, I would take it out and count it. From there I would know how much I had, and how much more I needed. I would never spend more then $125 total, so sometimes it took crafty ideas. One year I gave my best friend a scrapbook of pictures of the two of us over the years. It cost me about $10 to produce but gave us a great laugh.
Who says a kid needs the most expensive toys to be happy.
Why not start a new tradition...put a cap on the amount that you will spend per child. Tell them they can have whatever they want (age appropriate of course) as long as it is less then the set amount. This really makes kids learn about needs vs. wants and to be thankful for what they do have. Or do what my best friends family did (she was one of 7 kids) each kid got $10 to spend on one sibling (randomly selected) and they had to have one heart gift. The heart gift was something that couldn't be bought at a store. She one year got a wallet with a portrait that her little had drawn for the photo spot. Simple, inexpensive, made her value her sister and made a memory that lasted forever.