Yes, you "can" dye belts so long as it's a natural/organic dye. You do NOT want to use anything chemical or solvant based. This will ruin the belt. Keep in mind that belts are specifically engineered to do 2 things. Stretch slightly in an accident, and save your life.
Can you change the design of a life support system? Sure.. Should you? Not unless you know what you're doing and you are sure it will not change the capability of the system.
dklawson makes a great point as well. Your belts are OLD. Just spend the money to get new ones. Seat belts DO have a shelf life. They are not good forever. In my certifications for first response, and military training, I've actually seen snapped old seat belts. "Old" belts from the 80's... They lose elasticity, and wear down causing them to thin out. So if 80's belts are considered old and fragile, think of what yours are.
Not looking to make you feel bad for trying to do it without breaking the bank, but this is probably one of the places to spend some real money.. it could save your life some day.