How about a double sided (two toned) binding, here are some links...
https://www.byannie.com/double-sided-binding/
http://www.instructables.com/id/Two-Tone-Quilt-Binding/
http://www.evergreenquiltersguild.co...%20Binding.pdf

Thank you everyone!!! You ladies are so helpful! I've done the two sided binding before, I'd forgotten all about it.

If you make the flanged binding, you can put it on so that only one colour shows. I have often done this when I just don't have enough fabric for a binding. It is sort of like a facing on a neckline. Just make sure to press the seam to the narrower fabric.

I would never have thought of that. I just love this place. We get so many good ideas from each other.

minibarn- this what I was thinking of also, but would not have had the links. Sounds good for this situation, especially!

Very interesting concept, two bindings....

Or, you could do a single thickness of two very similar colors. attaching them both at the same time. I personally think when you have double thickness bindings, they don't wear thru as quickly.

look forward to hearing/seeing what you decide to do.

I would like the measurements for a two color binding that the colors meet on the edge of the edge of the quilt. If I n a 2 1/4 I guess Iwould nee 1 1/8 for each color. Have seen directons somewhere but can't find them today.

You'd need 1 1/8 plus 1/4 for the seam allowance, so 1 5/8" cut strips.