How does injecting low doses of allergens cure allergies?
But are there ways to tell the body that this allergy is safe and there is no need to amount a response to it?


Yes, that's what allergy shots (Exposure Therapy) does. Exposure Therapy is an effective, albeit sometimes imperfect, method of letting the body know that a substance is common and that it shouldn't mount a response to it. Over time the body re-calibrates itself to accept the allergen, although in some cases it's never fully accepted.

A complete "cure" can be attained via allergy shots, but the extent of the therapy's success will rely almost exclusively on the individual's immune system. Some people can be cured completely, others will never be cured.


  If not, why not?


There will probably not be a general "allergy" cure anytime soon because we're still not 100% sure why the body responds in such an overprotective matter sometimes and not others. Even if we fully understood at some point, there are many ways which the immune system can go awry that result in allergies. 

There isn't a single, double, or triple point of failure along the line - just about any immune cell, whether Mast, Eisonophile, T-Cell, T-Reg, B-Cell, etc. can misidentify a substance and contribute to an allergic reaction (although some are more likely candidates than others). More than that, just about any substance can become an allergen for people. There's a well-studied case of a woman who became allergic to Copper because of repeated exposure via an early version of IUD that she had implanted.

So with nearly every immune cell capable of mounting a response, and nearly anything in the world capable of provoking a response, the best route - at least thus far - has been repeated, increasing exposures to teach the body what is "OK" and what isn't. The absolute best way to avoid allergies later in life is to simply promote outdoor playtime and a widely variable diet to children while the immune system is operating at peak efficiency and learning capability.