My daughter belonged to the International Order of Rainbow for Girls, which is a girls group (11 to 21) sponsored by the Masons. Before she matured out, she was really into rainbows and rainbow colors. The girls made long cotton dresses for Grand Assembly (state meeting) every year. As long as the colors were primary, at one point in time or another any design was used. Some years the traditional rainbow was used. Other years, license plates, birds, jungle animals, bugs, you name it.... were used because the material available had all of the primary colors.
Bottom line... ask your friend's daughter to describe her "rainbow" quilt to you... is it the colors or the pattern or the picture/photo she likes the most?
That will give you a good idea about what direction you can take to make her really happy.
Best of sewing fun to you. Let us see what you come up with.