Installing a Bottle Cage without Mounting Screws/Threads
The approach I've seen is to use hose clamps to hold a bottle cage to the frame.  Hose clamps are what (used to?) attach a car's radiator hose to the radiator, if you've seen that.  If you have an old inner tube, you can slice that into strips to pad between the clamps and the frame so the paint doesn't get scratched.