Grinding coffee beans in the Olde Time Nut Grinder, now sold by Hampton Farms?
I would not expect it to work well.  It might not even work at all.
Nuts are very oily, relatively difficult to crush, and when crushed do not immediately become powder, but tend to require extended pressure and grinding to reduce them to a paste.  Once pasted, they need to be pushed out of the machine with some force.  Presumably the Hampton Farms grinder does all of these things.
Coffee beans, on the other hand, are moderately oily to dry, are delicate and crushed easily, and can be reduced to a fine powder in seconds.  Once powdered, they fly out of the machine on their own.
You can see some of the difference in the burr mechanisms.  Here's the peanut grinder:

And here's a conical burr grinder:

As you can see, those two grinding burrs are very different in design.