Is it possible to Breed an Animal to have more Females than Males?
Yes.
 What you are looking for is a meiotic drive, it's a genetic factor that favors its own transmission. Sex linkage is very common in these due to sex chromosomes not undergoing recombination. Once such driver, R2D2 (I shit you not) is a Y linked gene that drastically increases the number of male offspring in a mouse that carries it, to the point it can cause a population collapse from lack of females. 
Several such drives are known, none quite as drastic as R2D2.