When my son was smaller, I liked a small backpack for a diaper bag. I was given a very nice diaper bag but barely used it because it was so bulky. I know several others who also liked backpacks. So you might try feeling out the prospective mother or grandma about that first and see if she would get much use out of one. I do like the one that Mama Bear linked too, though. It doesn't look so much like a diaper bag.
Now that my son is older, I carry a small pack of wipes and a couple of extra diapers in my purse. My purse is pretty big, though.