Way 1 · best default
I'm really busy at the moment
Clear and polite. "At the moment" tells people it won't last forever.
Examples
I'm really busy at the moment, but I can call you on Friday.
Sorry for the slow reply, I'm really busy at the moment.
In a conversation
A: Do you want to come to my barbecue on Saturday?
B: I'd love to, but I'm really busy at the moment. Can I let you know?
Common mistake
Not: I have no time.
Say: I'm really busy at the moment.
"I have no time" can sound like "I have no time for you". Adding "at the moment" keeps the door open.