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Perhaps this bulbous terminal sans-serif brand-logo lettering would be what would happen if Cooper Black lost its serifs.
Don

Maybe: http://www.myfonts.com/fonts/typejockeys/freude/
Or: http://www.myfonts.com/fonts/eurotypo/talks/

Fairly close except it does not have concave sides: Frankfurter Medium by Alan Meeks
http://www.myfonts.com/fonts/linotype/frankfurter/
Could be edited to make the sides concave. With this change and some minor tinkering it is possible to make something fairly similar to the lettering in the logo.
Don

Some similarities in the lower case: PT Karolla Black http://www.myfonts.com/fonts/paratype/karolla/
Also: Debusen http://www.myfonts.com/fonts/typodermic/debusen/
Don

This could perhaps be an older version of the brand/logo?

Don

Probably a custom logo. I like Milk (but slanted) and Terylene. If you something cleaner to customize, may be starting with Helvetica Rounded or VAG Rounded could be interesting (but probably very long).

Compare: Milk Bold

Milk Bold left skew 15 degrees
Terylene

Helvetetica Rounded Black
working link:
https://www.myfonts.com/fonts/linotype/helvetica/
VAG Rounded Black

Don

Not to forget the bulbous Doobie:

https://www.myfonts.com/fonts/canadatype/doobie/
Which would be a very free-form rendering of Milkbar.
Don