Green’s Dictionary of Slang

(orig. US) don’t worry, it’s all right.

1963		Dundes ‘Amer. Indian Student Sl.’ AS XXXVIII:4 271: No sweat means ‘no problem’.
1973		J. Godey Taking of Pelham One Two Three 222: ‘It might get stiff after a while,’ Ryder said. ‘No problem,’ Steever said. ‘I can hardly feel it’.
1986		S. King It (1987) 623: No problem, Bevvie.
1989		Viz June/July 42: Okay Tom! No problem.
1997		E. Little Another Day in Paradise 133: No problemo, right guys?
1999		K. Sampson Powder 48: No problem, James. But will you just do me a favour?
2000		T. Blacker Kill Your Darlings 231: No problem, Greg, I said.
2003		N. Griffiths Stump 62: No problemo.