It will still be in the genitive case, because of the negation (nothing to do with the demonstrative adjective, possessive pronouns etc.)
"Oni nie lubią tej kawy (gen.)" - this coffee "Oni nie lubią jej kawy (gen.)" - her coffee
I hope I got the right word for "her" here, but if not the point is that it has no effect on the case of "coffee".
In fact, its the other way about - the case of the noun decides the case of any adjectives or other modifiers (is that the term?) like "this", "hers" etc.
Plus, even if positive - it would never be as written above in Accusative, would it? My keyboard doesn't allow me to type the "e" and "a" with the tail...so, in other words, if it were the positive statement: They like this coffee, wouldn't it be "Oni lubia (with a tail) TA (a with a tail, not E with the tail) KAWE (E with a tail", Correct?
Almost. It IS "ę". Even if a lot of natives would make a mistake of using "tą".
For "ta", the Accusative is "tę" and Instrumental is "tą". It actually should be very easy to remember, as it perfectly agrees with the feminine noun with which it works: Accusative "tę kawę", Instrumental "tą kawą". But a lot of people forget about it. Which doesn't make their version correct, anyway.
For "tamta" however, both Accusative and Instrumental are "tamtą". Also not hard to remember.