No way you are going to get any significant amount of the Router's 40 or
50 mW of 2.4GHz signal out the other end of 800 feet of that cable, be it
RG59 or RG6.

Three options come to my mind at the moment. 1) try a high gain
(directional) WiFi antenna at the outbuilding end only to try and get a
signal. MFJ makes a tiny yagi for that purpose. 2) possibly obtain
another WiFi Router or bridge of your own and connect it by ethernet cable
to a port on the owner's router, thus having your own wifi router to play
with by adding directional antennas, etc. 3) install a wifi bridge unit
somewhere in between the two locations...

I believe there are possibly other ways, too, but I haven't had my
morning coffee yet, so that's all I can come up with at the moment.

Ed