Does the umbrella have a tag? Can you tell what it is made from? If it is canvas, I would ask at crafts store for canvas dye. They can also tell you how to use it properly. If it's synthetic, it might be trickier.
If you don't mind the fabric being a little stiff, you can always use spray paint to spray the exact brown shade you pick out. Last resort. Sounds like you keep it open most all of the time. I don't know if there is a fabric dye strong enough to change from hunter green to chocolate brown. ONce the paint dries, it will be more water repellant. A twofer (2 for 1).
Pam D. is most correct...Spray paint is the best way to change the color of your umbrella...
Thanks for the info.