The car dealership was giving away ______ replicas of its most popular sports car as a sales promotion.

The correct choice is "miniature," which refers to a representation or model that is much smaller than the actual item. In this context, the term is used to describe small replicas of the sports car, which are typically created to be visually similar to the real car but in a smaller form. This makes "miniature" the most appropriate word for a sales promotion, as it implies a collectible or promotional item that showcases the car's design.

The other options listed do not correctly convey the intended meaning. "Minature" is a misspelling, while "minercher" and "minacher" are not recognized words in the English language and do not relate to the concept of small models. Thus, "miniature" stands out as the only accurate choice for describing small replicas.