i think you're going to find a lot of speculation on this forum.
i know this'll sound vague, but try to be balanced.
i do workout, but not "for" tennis. i make sure to do squats, lunges, legs presses, and the regular routine (bench presses, shoulder presses, tricep/bicep workouts, crunches and back workouts). the key when it comes to exercising the core is to do both abdominal and back.
i think you do need to workout for tennis, but only because it's important to keep your body fit and strong.
in terms of duplicating what goes on a tennis court to increase my stamina, i jump rope and do sprints the way a game may be played. for example, i'll jump rope slow for 40 seconds (like a slow rally) then speed up for 5 seconds (catching up to a drop shot) then go slow for another 10 seconds.
jumping jacks hammer your calf muscles (the side ones, don't know what they're called), so they also work for stamina/conditioning.
the same with sprints. i try to make it as random as possible each time. it works for me; but i'm no doctor!