Wildlife dept here put out a camera by a coyote den. Parents brought in 22 dead fawns that single Spring for the pups to eat.
I had one ADC professional tell me that the numbers had to be reduced by 75% to keep the population stable from year to year.
I look at those coyote pups as being the same as the prison guards at the Concentration camps in Nazi Germany during WWII where they were murdering people by the thousands.
If the rancher wants you there hunting to reduce coyote numbers, it is your obligation to kill them. You can only hunt them so much in one place before they get too smart to kill. Remember that 60% of the coyotes you kill are this years yearlings, the adults are more often than not too smart to call in for all but the most experienced hunters/callers.
There maybe laws regulating how you deal with pups in a den, check your local regulations or call the Game Warden who will also more than likely be willing to fill you in on the depredation of deer, calf, and turkey by coyotes in your area.
Wolves and coyotes are at the very top of the food chain, and they will tip wild life numbers out of balance in a hurry, given time. In Az during the 1950's, coyotes almost completely wiped out the Antelope and Elk populations. At that time, 10-80 was a legal poison, and Arizona knocked the coyote numbers way down with the 10-80, this is an interesting study for any that are interested.
Depending on where you live, the Fur maybe not worth saving at all, but the Wild life down the food chain maybe well worth saving...something to think about. In semi-rural areas, people's pets are a natural part of the coyote food chain.
If it were me, I would tell the rancher where the den is, leave it up to him which could be a win/win. The rancher loose respect for you in that you did not kill the pups, but you will learn where he stands. Late July or early August, you can go back and likely call at least some of them in and educate the rest of them. You still need to check on the laws concerning the "Den" issue. The Den issue varies from state to state.