We did a party at the Mcdonald's playland one year when I was in a crunch, and I didn't send an invitation, I made a phone call and made it feel more like an infomal gathering. I told them not to bring gifts as it was just a playdate for her birthday, and I would bring cupcakes. We only invited closest freinds, (4).
What you can do is say on the card "In leiu of gifts, please make toy donations to a local charity of your choice." Or put "ressession Buster Birthday - used toy swap" in the card, as one mom said- what a great idea. Bring one old toy and every child goes home with a new one. That way she won't be bombed with toys, and when she looses interest, you can just donate it to charity. Guarantee that will be a popular option among those attending! Each child will go home very happy to have attended and the moms will be happy too. It will teach your child the joy of sharing and caring instead of getting.
I've always hated going to those parties where there is 25 kids and a 20 foot pile of gifts and the kid opening them throws them over their shoulder to open the next one. We always keep our parties very small,...2-3 kids. and then I don't have to worry about piles of gifts. If someone asks what my child needs then I have a suggestion that is 10.00 or under, like socks, art supplies, a pad of paper, bird seed, a packet of flower seeds, ect.
Good luck.