I buy the prefolded diapers that have a thicker portion down the center. You can find them at places like Target and KMart. In case it has been awhile since you have bought diapers, don't have a heart attack when you see how the price has gone up!
Cut a strip of fabric slightly wider and longer than the thicker middle portion of the diaper. I am guessing I had a strip 18 inches long by about five inches wide. Press the sides carefully, and pin over the middle part of the diaper. Fold the ends under and press. Stitch on the edge of the fold, and you are done. Takes two minutes, seriously.
A couple of these that coordinate with your baby quilt would be a welcome and super cute little extra gift to give the new mom.
And if you want to skip making a baby quilt, just make burp cloths out of the whole stack of a dozen diapers! Sure would save you a lot of time and money.
This is a stack that I made for Eva before she was born. We used them to pieces!