At foursquare.com, if you go to the user profile for that user, there is a drop-down that lets you set the notifications you receive from that person.
Simply set that to "Off" instead of "Always On" or "Nearby" and you should be good to go.
On my Android, if I go to the "Profile & History" for one of my Foursquare friends, there's a button directly under their photo that looks like a vibrating smartphone.
Tapping that brings me to the "Push Notifications" screen, which tells me what notifications I'm getting from the person, with a button labeled "Set push notifications".
Tapping that button gives me the option to see what notifications I get from that person:
Same as above.
(I expect the iPhone version of the app is very similar.)