I used to use Worcestershire all the time, but it contains soy. So do most marinades. The first time I cooked rabbit I went looking for recipes, and found a marinade that turned out to be a great replacement for Worcestershire. This tastes great with chicken, beef, or venison. I think I used it for squirrel too.
1/2 cup apple cider vinegar
1/2 cup molasses (optional)
1/2 onion, sliced or chopped (optional)
1-2 tsp garlic powder or 2-4 tsp minced garlic
1 tsp rosemary, crushed (optional)
2 tsp salt
2-3 cups water, enough to submerge meat
Mix all ingredients and pour over meat. Refrigerate for a few hours or overnight. Cook meat according to your preference. I like to bake it in the marinade, with rice or chopped vegetables, covered.
Variations: in place of garlic, use cinnamon, mustard, or other favorite spice. Or use multiple spices. 1/2 hour before meat is done cooking, add some cranberries, prepared as for sweet potato casserole, or some raisins.
For low-FODMAPs, leave out the onion and use different spices in place of garlic. For GAPS or SCD, use honey in place of molasses.
Loosely adapted from first recipe here: http://www.thetastespot.com/the-taste-spot/2011/04/how-to-cook-rabbit-5-ways.html