The original was a Cortefiel, made in Spain in the early 1960s, so you can pretty much forget getting that exact model.
Your best bet is to try the Salvation Army, or Goodwill, or any other used-clothing outlet. The more "used", the better.
You'll find a very detailed description in the "Columbo's Raincoat" article, in the Scrapbook section of this site. But, for purposes of reasonable authenticity, and to be recognizable as Columbo for the non-experts who will see you, it's sufficient that the raincoat be single-breasted, and preferably quite short. (Please do not wear a Bogart-style, double-breasted, belted trench coat as Columbo.)
It's a big plus if you can find one with lapels that resemble a suit-jacket's lapels (instead of the simpler, shorter collar on most single-breasted raincoats), but I wouldn't count on finding that. Even better if the pockets have flaps, or if it has the hard-to-get "french cuffs" with buttons.
Like I said, get it single-breasted, short, and well-used, and you'll look fine. Have fun!