No, I'm sorry, but nothing doing.
Wiktionary has an entry sourced from a 110-year old enormous dictionary, with one usage example, from the 1660s. The OED also has an entry, with the same quote from the 17th century. But in the OED the word is hyphenated.
Are there examples from more recent times of the use of the word coefficiency? Yes, there are a few. But every single one, as far as I can see, is mistaken, where coefficient is meant. In the News on the Web corpus there are mentions of "drag coefficiency" - that should be drag coefficient. Likewise "correlation coefficiency", "coefficiency of performance" and "Gini coefficiency". There are no examples of the plural coefficiencies.
I'll take the OED's word for it that coefficiency is a word (with a meaning different from coefficient). But it's so dated and obscure that nothing would be achieved by adding it to Chihuahua.