Rifle bullets tend to shoot pretty flat to their zero range, then drop of quickly beyond that point, but zeroing for a maximum point blank range requires the size of the target to be taken into consideration. While you can zero for 250 yards for less drop at 300, you might be confounded if the maximum ordinate takes you off target at some mid-range point. If you don't know the exact velocity or your bullet's BC, the best advice is to get out and experiment with 200, 225, and 250 yard zeros to see which benefits you the most at longer and at shorter ranges. Confirm your long range zero, but also confirm that your 150-175 yard impacts are within the size of your target. You will find though that correct range estimation is very important, and close enough usually isn't.
If your scope reticle has hold-off points, those can be used to manipulate trajectory. For example, with a duplex reticle, the bottom of the top post might be in coincidence at 100 yards, when the scope is zeroed for 250, and the top of the bottom post might be in coincidence at 400 yards. Bracketing a target between those points and the center cross-hair might give you 200 and 300 yard zeros respectively. While the exact values will depend on your particular scope and reticle, and the height of your scope's center above the bore's center line, it is something you might find useful in the field.
Be sure to record your drop at 100 yards and at your longest impact range. If you have these two points correctly worked out, you can work backwards with a ballistics program to determine the drop at any range between those two points. Ensure that your long range bullet drop does not include an error. For example, lets assume your theoretical drop at 300 yards is 7", but the holes in the paper seem to be 10" low, that suggests your BC, velocity, or range is something other than you thought it was. Manipulating the BC on the ballistics program should correct the prediction errors, if the range and velocity estimates are correct.
If you don't have a laser rangefinder, get one. Not knowing your specific BC or velocity is one thing, but if your range estimation is off significantly, your presumptions concerning trajectory at any given range will be inaccurate; tweaking the BC on a ballistics program won't remedy the problem. When you're actually hunting, the LRF will be useful for marking specific landmarks so you know when the coyote is at a certain range. Its 230 yards to that rock, its 175 yards to that tree, its 440 yards to that fence line, and so on. Once the coyote passes any of those pre-ranged landmarks, you will have a firing solution already worked out. That is much easier than attempting to work out the bullet drop on the fly, as the coyote lopes past you.
