Prepare all the vegetables and place them in the bottom of the slow cooker. In a small bowl combine the beer, chili sauce, minced garlic, and brown sugar.
In a large skillet over medium-high heat, using the oil, brown the rabbit on all sides. Arrange the rabbit pieces over the vegetables in the slow cooker, and then pour the beer mixture over the rabbit meat.
Cook on high heat for 3-4 hours (if you need extra cooking time-cook on low 5-6 hours) or until vegetables and rabbit meat are fork tender.
Drain the juices from the slow cooker to make gravy. You should have about 1 1/2 cups of liquid, if you don’t, add some water to make up the difference.
Mix the flour with the cold water until smooth, in a small saucepan bring the juices to a boil, and thicken using the flour mixture.