You could always make a 'flange' binding. Or 'line' the binding. The measurements are the same but the fabrics are opposite for flange as to lining. For a 2 1/4 inch binding, you will need 1 1/2 inch wide strips of your preferred fabric and 1 1/4 inch wide strips of your alternate fabric. Once you sew the strips of each colour together, you then sew the two strips together and press in half. For a lined binding, you would lay the binding with the narrower strip up, on the front of your quilt and sew. Then finish as usual.