Usage of 'vernacular'
Solution 1:
The answer by lbf clearly shows that vernacular is sometimes used for a jargon a particular profession, and that such use of the word can be found in respectable sources. It therefore cannot be dismissed as incorrect.
The OP’s hesitation to so use it nevertheless manifests a sound linguistic intuition. Using the word in this way is in conflict with how it has been used traditionally. In its original sense, the word stands for the language spoken by ordinary people, i.e. people without specialised education. Its primary purpose has been to contrast such everyday language with the ways of speaking that can be understood only by those who are initiated into a particular field of knowledge. Saying that something is a vernacular has traditionally implied precisely that it is not jargon. I suspect that it is used for a jargon of something like psychology only by those who are unfamiliar with its original meaning. Although such use can be defended, as was well done by lbf, it may be prudent to avoid it, because it is likely to rub the wrong way those who are familiar with the original meaning of the word.