Sorry, something suddenly came up tonight so I have to raincheck on the meeting. Sorry, have a great weekend.
"Raincheck at some other time" isn't correct. I can understand what you mean but it doesn't sound natural. Here's one way to think about it: to take a raincheck, or to raincheck, is to take out a debt on the event instead of attending at the planned time. You'll repay the debt by attending or holding the event at a later time. You don't take out the debt at a later time; you take out the debt now and repay it later.
"Raincheck" is informal and nuanced, and personally I would only use it here if the meeting is very informal or casual, and if your cancellation doesn't strongly affect the other person. Otherwise, to me it feels a little presumptuous and not very apologetic. Instead, I would say, "I can't make it to the meeting," "I'll have to miss the meeting," or "I'll have to reschedule the meeting" (if you were the one who originally scheduled the meeting).