you wont need a bull barrel gun for 300 yard coyotes.I shoot a ruger m77compact with a 16 1/2 inch barrel and leupold 4x12x40 scope the whole rig weighs a little over 7lbs and I have made some 290yard shots on groundhogs off of sand bags with it before.It is a 223 caliber,which I would reccomend if you like to shoot alot the ammo is cheaper,the 22-250 is capable of shooting alot farther but if 300 is your max range on a songdog then the 223 is perfectly capable of doing it.I have a remington 700sps in 243 and it shots sub-moa with the federal fusions so I think that this gun in 223 or 204 or 22-250 would be a good coyote rifle and you can get a remington 700 trigger adjusted by you gunsmith,Good luck!!