Coyote Hunter gave some good points..at really long range a 140 will carry better, but the lighter bullets are safer if you have any safety concerns at all...I would have to look back at my notes, but 120's would clip along about 3500 fps out of my 7's, but they all have atleast a 26 inch barrel on them..sometimes one powder will out distance all others with a certain bullet wt..but experimenting is required...one bullet I thought of that I shot years ago that was fairly accurate and very explosive and cheap, was a Speer 115 grain hollow point...I think if I were you, I would look at either 120 grain Horn. hollowpoints, or 120 grain Nosler btbt.. If you want a coyote load, they should do it..while a 140 or 160 would carry up better at 500 or 600 yards with more power and less drop, in reality, you will probably shoot most of your coyotes between 100and 400 yards...the 120's should perform very well and with a high degee of blowup...You are right, you would be better armed with a .22-250 or Swift, but shooting the 7mm with light bullets, beats not shooting at all..I am not sure where you live, but here in Wy. I almost always carry a .22-250, an Improved, or a .220 Swift...for much of my shooting they are perfect, but the wind is a big factor in somedays selecting a heavier caliber..and if there is NO wind the heavier caliber will still kill coyotes fine...but if you are really going to get into coyote shooting, then a big .22 should be on your list of I MUST HAVE THIS TO LIVE A GOOD LIFE....
My favorite even though I have shot .22-250's when they were still a wildcat, is the .220 Swift..just something to consider for NEXT CHRISTMAS or you birthday...take care, and good shooting......