Sounds like you are talking about a fenced herd. If thats the case and if it were me, I would be looking to maximise the opportunity and not waste any meat either. I would go the head or high neck shot with a very accurate rifle, even a 223 or similar. Spend a lot of time finding the best position to get a good shot and not stir the deer up too much.

A mate of mine has a small herd of 50 fallow just outside of town and we spend a lot of time finding the best place to ambush an animal we want to take out and then make a great head shot. A lot different to hunting a wild animal but the great venison from a managed herd (better than wild fallow) makes it worthwhile. We usually use my mates 223 and from now on I am going to be using shooting sticks instead of a 'ready rest' to get the best shot we can. Even on his 30acre block it can be a REAL challenge to get the job done right... plenty of times I have driven home without getting the shot I wanted.... come back the next day.

JH has the right idea on head shooting (above)!!