Short Ribs questions

Try Merrill's recipe: https://food52.com/recipes/9109-short-ribs-with-beer-and-buckwheat-honey

I am loving the recipes from "Simply Ming One Pot Meals" and there is a really great recipe for aromatic short ribs with root vegetables. No tomatoes. I am really enjoying everything I have tried in the book so I can recommend this recipe. Hope you enjoy it!!
http://www.foodreference.com/html/aromatic-ribs30.html

A few more ideas on the non-tomato front:
*dry rub (Texas or other American, like Mike Mills)
*coffee dry rub (variation on above)
*recipe with pomegranate juice and/or red wine as marinade (see recipe from Chef Micah Wexler, Los Angeles)
*braised in beer (almost like boeuf a la flammande)

Yes, you can use boneless. It might reduce the time needed to cook the ribs, so check for doneness sooner. You don't want to overcook it.

As for non-tomato recipes, search for "Asian short ribs", the recipes tend to not have tomato or tomato-products. Here's a delicious-sounding one from Emeril Lagasse, http://www.foodnetwork.com/recipes/emeril-lagasse/asian-style-braised-short-ribs-recipe.html