You need to shoot them. As many as you can. You manage it for the good of the owner, not yourself.
Rabbits are survivors. If they do not get hit severely by disease, you are unlikely to completely clear them but you should be aiming to significantly reduce numbers. That is easier said than done.
I have shot over 400 rabbits this year on the golf course where I play and there are still tons there. It should get easier at this of time year as the nights draw in. You can pick and choose weather and conditions to suit whereas earlier in the year it is tough to be out so late on school nights when it doesn't get dark until 10pm.
How will you be removing the rabbits from the course? That is one of the biggest issues. Anymore than 2 or 3 and you start getting long arms and tiredness sets in quick. Do you have an outlet for them. They soon rack up.
I have access to a golf buggy if I want but I personally find it less effective than being on foot. I use a fishing trolley with pneumatic tryes with a plastic storage box bungee strapped to it. That allows me to get 30 rabbits off the course without killing myself and keeps me more mobile and quiet. Bipods can be a pain in the arse on undulating ground. You see something in the thermal when stood up and then you get on your belly to take a shot over 80yds and the target is gone as a hump is in the way.
I sometimes take a bucket seat with strap on and some shortened bipod sticks to enable me to shoot accurately out to 100yds or so. The bucket seat also has pockets on so gut hook, gloves, knife, spare headtorch, hand torch, batteries, ammo etc can go in.
The HMR is the tool of choice usually but I sometimes use the .22LR in places where there are a couple of houses so I don't disturb anyone.
Do not underestimate how difficult it is to gauge distance at night. I shoot lots at night on my own land as well as with friends on their permissions and am also a proficient golfer who knows this golf course like the back of my hand. It is still very very difficult to shoot a .22LR with killer efficiency if you do not know if a rabbit is 50 or 90yds away.
I would imagine the Pard LRF scope would be perfect for the .22LR on rabbits but I use an HMR with a a digex atop. It is very very effective as much of the time you do not need any IR which can spook rabbits quite easily. Just point and shoot out to 120yds.
Be safe, fully familiarise yourself with the boundaries and what is beyond them. It is easy to feel that the cover of night provides a blanket of security. It doesn't. For every shot you can take, there is another you cannot. Also consider your spent cases. When shooting high volume, is the owner ok with daily golfers finding brass cases on the fairways and tee boxes? You would be surprised how many golfers curse the damage that rabbits do but then balk at the thought of someone shooting them. I catch every ejected case I can and take them from the course.
Golf courses can be highly productive areas to shoot but it is hard work to do correctly. Good luck with it
If you want to do the owners even more of a favour, buy a multi LED UV torch (they are less than a tenner on fleabay) and search about in the rough (160-220yds from each tee on the right hand side is a good place to start) for balls. They stand out like beacons despite you being unable to see them at all in daylight. With premium balls costing £40 a dozen, you can probably provide the owner with some balls which he can sell on. It is likely to help you keep the permission forever. You can find a coupla hundred balls in a hour if you look in the right place.
The foxes follow me around and it is a job to get to the shot rabbits before they beat me to it. I am not shooting the foxes but if I was, I would be shooting a rabbit, leaving it in situ with a slit belly and then waiting in ambush for the foxes. To start with, it would not surprise me if you shot plenty of foxes initially. I see loads where I shoot. Literally double figures on every outing. They steal loads of my rabbits.