Are there any kinds of drinks that can counteract the effect of antibiotics?

Anything with alcohol in it.

Depending on the tablet milk can slow the rate of absorption

Yes – the alcoholic variety…

If you mean the negative effects of antibiotics, then try a probiotic drink of some kind.
Yoghurt perhaps.

Hemlock? That will counteract the effects of just about anything – ask Socrates.

Alcohol does not affect the mechanism of antibiotics, contrary to what has been mentioned above. Certain antibiotics (like metronidazole) can interact with alcohol resulting in a disulfiram like reaction, which makes you feel ill.

You should check with your doctor or pharmacist, since the metabolism and/or absorption of some antibiotics is affected by when and what you eat.

You can find some helpfull information both here and here.