Is there a “Milk Pitcher” style trick that looks like a “Coffee Pot”?

You mean, like a round Bunn Coffee pot?

Look at all the pitchers out there, They all have straight sides, There's a reason for that, So I would say no, probably not.

But there was a gold water pitcher that worked like a lota which was made.

Actually, there are straight side cylindrical coffee pots. Some of the Mr. Coffee pots are. Styles evolve, but a trip through a few thrift stores or flea markets is likely to unearth one. Gaff it up and you'll have a nice trick that I doubt anyone else is doing. Making the gimmick might be your biggest hurdle.

Nice idea!