Here's the good news: Foster parents can claim a child they fostered as a dependent on their annual income taxes if that child lived in their home for at least six months plus one day of the tax year. That's six months plus one day for each child. If you had child A live with you for four months and child B live with you for three months you can't claim either of them. I'm also told that if audited you need to be able to show that you spent at least twice the monthly stipend on caring for that child, which is usually easy to accomplish when you factor rent/mortgage and utilities.
Here's the bad news: If someone else claims a child before you do, your tax return will be denied and you'll have to jump through some additional hoops and wait a couple extra months while the tax man sorts it all out.
The lesson? Get your taxes filed as early as humanly possible! I know, I know, you're thinking, "Those bio parents can't even manage to figure out where to get a bus pass so that they can make it to a scheduled visit with their child, they won't ever figure out how to file their income taxes!" Ha. Think again. File early people. Take it from me. We don't get many benefits as foster parents (not tangible benefits, at least), and we can't afford to let this little year-end "bonus" slip through our fingers.