I only think of a funny response minutes or hours after a conversation has ended.

That's good actually. It means you have a sense of humor, just miss to opportunities. So, really you just need to prep more and anticipate.

Really, the whole perception of being "witty" or "quick witted" is largely an illusion. Most witty retorts are well practiced and prepped, and witty people get good at knowing what directing a conversation will go and I ready. The real secret every professional comic and writer uses is hyperbole. It's basically the ability to find absurd humor in things most people overlook. And people who are funny to be around - whether they know it or not - likely picked up on as a child and exercised it growing up. Some children were exposed to it by their parents. Many comics talk about how they grew up in environments that enjoyed hyperbole and verbal/written forms of word play. While there's a genetic component that make some comics exceptional, there's still plenty of ways the average person can get in on the act by practicing when you're alone making ridiculous connections when you go shopping or traveling, and using it on strangers. That way, no laugh - no loss.

I'll give you an example of a great shot I got in just last week using hyperbole. Most of us know the old Groucho Marx line: "I once shot an elephant in my pajamas... how he got in my pajamas I'll never know." It's a perfect gem of hyperbole humor, because our brains are forced to create the absurd image of an elephant in pajamas.

So. I was sitting with friends talking last Saturday night when my friend's wife told a story about how she jumped out of bed and killed a brown recluse spider wearing nothing but her panties. My mind jumped to the Groucho joke and I quickly replied: "...and how a brown recluse spider got into your panties we shall never EVER know!" The room ROARED with laughter several minutes as everyone started joking about a spider wearing panties. (I was actually shocked it went over so well.) I'm no great comic, but I like to make people laugh. Humor 101 is all about employing the clever use of hyperbole - forcing absurdities into the mind before people have time to process it. So my recommendation is practice looking for hyperbole in everything you encounter. It won't always work or seem funny, but the more you do it the more absurdities your brain will start connecting to general situations. After that, it's just have the balls to throw it out there.