How many times do I have to use Yojimbo to get his compatibility with Yuna high enough for him to reliably use Zanmato?
Strictly speaking, Yoj will never ever
reliably use Zanmato, even if you two are the best of friends. You could have 255 Compatibility, pay him 999,999,999 gil and have him target a Dingo, and there's still a chance he'd pull a Kozuka on it.
I think (not sure though) that he starts at 128 Compatibility. If he uses Wakizashi (his second-strongest attack) or Zanmato, his Compatibility will rise by 3-4 points. If he uses Daigoro or is dismissed, it will decrease a little. If he dies, or especially if Yuna pays him 0 gil, it will severely decrease.
Basically, pay him a lot when you use him to give him a better chance to doing stuff that will raise his Compatibility. If you're careful about it and give generously, then you'll see Zanmato more and more on average - but it won't ever be close to a sure thing. The power of the foe you're facing, as well as the Random Number Gods, have about as much of a hand in things as carefully raising Compatibility.