Contact a local Quilt Guild or two and let them know what you are doing. We usually get a couple of quilts/shawls every month or so from those wonderful ladies. Do an online search for prayer shawl/quilt. We do 45"x60" as a general size. Non-sewers in our group do a Linus Project type fleece blanket in that size. Rail fence, D9p and Jelly roll are 3 easy/quick ones. Non-sewers also just take two lengths of fabric, sew up pillow case style, turn, stitch around edges and hand tie. Fannel is a good backing because it does not slip off beds or laps as easily. Good luck, be patient!! It is a wonderful thing you are doing and such a blessing to others and yourselves.
There are also books available at amazon.com about prayer shawls and ministry that are full of great info and inspiration.