Do you have a local quilt guild? Especially a state quilt guild? You could contact them for the names of people who might be willing to make and donate a raffle quilt for this child. I think your best bet is to find an experienced quilter who is willing and able to make a bed-sized quilt quickly. Check the raffle laws in your state to make sure you do it legally.
Our quilt guild makes a raffle quilt every year for the quilt show, to help fund it. Members buy and sell a lot of raffle tickets for it at $1 each. I think this is one of the easier ways to make money for a charity, especially if you have some good ticket sellers in your community.