Get Your Dog Care Questions Answered by Experts
Normally, with a healthy dog, I'd be suggesting fasting and feeding a bland diet to help the dog get over this bout of diarrhea and vomiting. With a diabetic dog, however, things get a little more complicated.
What I'm most worried about with this guy is DKA - diabetic ketoacidosis - which, as I'm sure you know, is a complication of diabetes. More information on DKA can be found here: http://www.petplace.com/dogs/diabetic-ketoacidosis-dka-in-dogs/page1.aspx .
My honest suggestion here is for you to get your pup checked by a vet as soon as possible. I understand that it's the weekend and that your vet is out of town, but if there is an emergency clinic in your area, I think it's best that you visit them. They'll be able to rehydrate your dog and most likely give some medications that will at least stop the vomiting so that your dog can eat something (which is, of course, an important part of managing diabetes).
I hope this helps.