Looking at Remington factory ammo data, they have 80, 95 and 100 grain bullet options. All would be appropriate for shooting coues deer. Based on Remington's ballistics, it looks like you can shoot all of them out to 300+ yards.
If you were to reload for your rifle, you could probably develop a load with 400+ capability.
First off you can only shoot as far as he is capable of...practice practice and then when your all done...practice some more. Energy don't mean squat if your not puttin it where it is supposed to be.
Put your numbers in a ballistic program. I'll run out to where I hit 850-900 lbs of energy (minumim!). Based on your speed and bullet his will vary. Be sure to use the correct bullet for your application also.
From my 243 with a short barrel I can push a 95gr NBT to 3050 with H4350 and keep accuracy. For me, 600 is as far as I'll go. I'm very comfortable to 400 and would start really thinking things through before going into the 400-600 yard range. But that is ability as much as effectiveness.
I would look at the NBT's, A-max's and Bergers for your best long range performance.
This past weekend was the opener in Nebraska for deer. We were hunting by Chadron in the national forest. I shot 4 deer with my 243 win one was 330 one was 610 and the other was 727. It was probly the only day in nebraska I would try a shot like that. There was no wind what so ever... Not even enough to move the long stems of grass!
The load I was using is 44.5 grains of H414 with a 87 grain Hornady V-max that load out of my rife shoots about 3300 fps.
I have shot over 20 deer with this rifle and load and 8 of them were at or over between 300 and 425 yards. The longest I have ever had to track a deer is 30 yards. From the typical sprint of death! The reason I choose this bullet is it transfers all the energy into the animal!
But like others have said it is not what you are shooting its where you put the bullet. My uncle has used nothing but a 22 hornet for the last few years keeps his shots under 200 yards and shoots them in the lungs or white of the neck and its a done deal! So practice practice practice!
Also never hold and hope on your target Range it, dial it in with the scope and take your time! Dry fire a few times to be dang sure everything is going to happen as planed!
My rifle is was build by bryant custom, 23 inch lilja barrel, with a fully blueprinted action and bedded in an HS precision stock with a jewel trigger set at 1 pound of pull.