What you've got at the moment is not good.
If you install your own tracking software do both parties need to be able to login to see the number of visits?
Or will they trust you and a print out?
Look at
StatCounter Free invisible Web tracker, Hit counter and Web stats, simply install the code on each page of your site (you'll need to pay statcounter to track unlimited visits), you can then give them a nice printout or even provide them with account login details to see for themself (but they then would be able to see all your other webstats!)
Statcounter off a free version, so you could set it up to see if it suits your needs.