A funny, casual alternative to 遠慮 is お断り. Technically it’s derived from the keigo（お＋断り＋します） of 断る（ことわる）, which means to reject or refuse, but I think the actual usage is more casual. It’s generally used as a terse method of shooting down an unreasonable request.
Daniel: 俺と付き合ってくれ！ Go out with me!
Sumiko Nishioka: お断り。 Hell no!
There’s absolutely no way I could get a date with Sumiko Nishioka, and she and the imaginary audience in my brain all knew that, which is why she frowned and okotowari’d me, causing the audience to laugh at my suffering.
It’s generally delivered in a flat, flat tone with an air of “I’m not amused, asshole.” Although the English “Hell no” is hardly ever delivered in a flat tone, the meaning is just about the same, and it’s also capable of generating laughter.
I’m convinced that part of the reason お断り is so funny is that it doesn’t have any of the trappings of Japanese politeness – no 残念ながら, no hesitation, no apologies. Compare it to the conversation with my supervisor below and you can probably tell that the second sentence in both have, essentially, the same meaning and are merely delivered in starkly different tones.)