No thanks works 99% of the time. If they persist, I found being honest works the best (imagine that....lol). I simply say I'm a recovered alcoholic (or, when I was new, "recovering alcoholic") and I don't drink anymore.
Why dance around the truth, ya know? The bs stories and excuses were just temporary fixes and that person would inevitably try and push it on me again later. There's some real freedom in telling the truth - both for them AND for me. Telling the truth also got me to look at a pretty valid question - why was I so ashamed to be in recovery? What was I trying to hide? Why was I still trying to play God and manipulate everyone's opinion of me? .......wasn't that they type of behavior I exhibited IN the disease......and wouldn't it make sense to do the opposite in recovery?