Training is normally used as an uncountable noun by native English speakers, and in this form it doesn't take a plural. However, some dictionaries list it as being both countable and uncountable, with the caveat that the countable form is little used. Google Ngrams shows the relative frequencies for both forms:
Interestingly, Google Ngrams indicates that usage of trainings is on the increase. Unfortunately, we have no way of knowing how much this is influenced by native English speakers adopting the countable form.
The Cambridge Dictionary and Collins Dictionary indicate that it is uncountable. The Oxford Living Dictionaries indicates that it is a mass noun. Wiktionary mentions the plural form, but says that it is not often used. Other online dictionaries offer no opinion. No online dictionary that I can find provides an example of usage as a countable noun.
I don't think that I have heard a fellow native English speaker use the countable form. If I have, it would be only rarely. My own feeling is that you should avoid using the countable form if you ever have ambitions of being mistaken for a native English speaker.
Google Books Ngram Viewer
Cambridge Dictionary: Training
Collins Dictionary: Training
Oxford Living Dictionaries: Training