Chop dandelions in small bits. Heat butter in heavy 2-quart saucepan and add garlic and greens. Stir over moderate heat to wilt. Lower heat and cook until tender, stirring often, about 5 minutes.
Add stock, water, and rice, and bring to a full boil, stirring now and then. Add salt, if needed. Turn heat to lowest point and cover pot. Cook 20 minutes.