Is it appropriate to abbreviate "congratulations" as "congrats" or "congrads", or are both acceptable? I have seen the latter used very often which is why I'm asking.
Congrads is an incorrect spelling of this abbreviation. Put Congrads in any word processor and it will return an incorrect spelling. This is because "d" does not appear in Congratulations. Unfortunately, many people ignore this and still use Congrads. If you want to stay grammatically correct, use Congrats.
Congrads is found just often enough to irritate people. A web-search will find people complaining about it, though http://www.collinsdictionary.com/submission/9542/Congrads is someone trying to actually have that form considered for inclusion in Collins' dictionary. The fact that they suggest it is short for "congradulations" [sic] points to this actually being a joke, making fun of the few who do spell it congrads.
Now, everything starts somewhere, so it's quite possible that at some point in the future, congrads will eventually make its way into enough usage that it will be considered "a real word" by the majority.
In the meantime, since there are people complaining about it, and no similar group complaining about congrats (bar a few who just don't like abbreviations at all), it would be better to stick to the form congrats.