Thanks to Valarie for this Frugal Baby Tip!
I picked up about five yards of vinyl for around $8 -- probably could have gotten it cheaper if I'd been patient enough to wait for a sale. With this I was able to make several bags -- one for each diaper pail and some smaller ones to carry in the diaper bag.
Making a bag is sooo simple. You just have to sew the bottom and side seam, then sew the top down far enough to make a casing to slip a cord through --don't forget to leave openings at the side seam. (I know, I'm not that good at giving directions. :P ) For the diaper-pail bags, I got fancy and custom-shaped the bottoms, but that's not necessary. I throw these in the wash with the diapers. I put them in the dryer for less than five minutes, just long enough to get the bulk of the moisture off. They've been working for me for 4-5 months now.
If I could do it over, I'd make less of the small bags to carry in the diaper bag, and make two identical ones to go in the diaper pail. So that I could have a fresh bag in the diaper pail while the other was being washed. Not that it's a big deal, but sometimes I get busy and washing diapers takes all day. All the diapers that I change throughout the day need somewhere to wait until my diaper-pail-bag is clean again. I rarely need as many of the small diaper-bag bags that I made, since I'm always home when I'm washing them so two would have been plenty. One day I'll get industrious and make some more.