Can baking soda be used instead of baking powder in a cornbread recipe?

It can be, but only use about half as much baking soda as you would baking powder.

Also, baking soda should be mixed with Cream of Tartar to help it work. 2 parts baking soda to 1 part cream of tartar works best. If you don't have cream of tartar, add a little vinegar or lemon juice (not more than 1-2 teaspoons of the juice or vinegar, though, so the taste of the cornbread doesn't change).

Cream of tartar, vinegar and lemon juice add acid, which the baking soda reacts with to work best in baking. Baking Powder already has an acidic agent in it, which is why you don't have to add anything extra to that.

If your recipe already has some kind of acid in it (which is possible - there are a lot of different cornbread recipes, and some call for acids like lemon juice or vinegar), then you just need to add the baking soda by itself.