Everyone else has covered the "he knows what he's asking for" angle, so I'll just say that I don't see anything wrong with saying in a friendly (friendly!) way, "Like a date?"

Some guys might be frazzled (particularly the ones using this approach for their own sake rather than yours), but I think a lot of guys would appreciate it -- they might feel less pressure to stick to the "casual dancing" approach. They'd also be less likely to self-rationalize later ("maybe she really IS busy washing her hair next Saturday!) and ask you again.

When they say, "Yeah, like a date," just say, "That's really sweet and I'm flattered, but I have fun being friends."

Plus, this way, if he decides he WOULD like to hang out with you just as a friend, he can ask again without any explanation.

I understand it depends on your level of comfort and confidence. If you think you can take it, being super-straight like this works out best for everyone all around.

I'd stick with your "no thanks" but then tack on something along the lines of hanging out in a group. Like "no thanks, but maybe I'll see you at Petunia's party next weekend. A bunch of people are going to be there, and it sounds like it'll be really fun!"

You could say "How sweet of you to ask! I'm super busy, so need to say no. Thanks though!"

Then run awaaaaaaaaaaaaaaaaaaaaaay!

Do you want to have coffee with him? If he were just a friend? Then say yes, and navigate from there. At the coffee, you drop some hints that make it clear that you're not interested in him romantically - bring up someone you have a crush on for instance. That will chill the air, but quick.

Another strategy could be to say "Yes, I'd love to- and let's have Lucy along too!" - Someone else you work with, that makes it clear you're not psyched to go out alone with him, but like the idea of being pals.

If you just don't want to have coffee with him at all, then say, "No thanks," politely, but firmly.

I agree with New York State of Mind.
But I see nothing wrong with your simple "No Thanks." You don't owe him any more explanation, and I would think if you elaborate more, it would be more encouraging that a simple "No, thanks."

Guys are taught that persistance pays off, and to continue asking, if they are interested. Therefore, I'd think it may take several answers before he picks up on the state of the "No"... if you know what I mean.

This is the kind of situation white lies were made for.

"Sure, although I am seeing someone, just so you know" -- if you want to hang out as a friend.

"Sorry, but I'm seeing someone, and he wouldn't be too thrilled with that" -- if you want an out.

If I were the guy, I'd way rather hear the white lie than "No thanks". Ouch!