What is the natural cure for cat allergies?

Avoid the cat :( Unfortunately, the only "natural" way is to avoid being around the cat :(. If you are allergic and you don't want to take medication, then an effective and natural alternative is immunotherapy (an allergist on an ent/allergist) can help with this. This is a process by which your body will naturally develop antibodies against the cat allergens over a period of time.
Quercetin. While there is no cure to cat allergies, natural symptomatic relief can be found through the natural mast cell inhibitor quercetin. In order for this to work effectively it must be taken daily before exposure and at doses 3-6gm (powder usually easier than capsules).