You could list them on Craigslist. Unfortunately rams are not much in demand, except for meat. A ram is half of your flock, he breeds the ewes and the resulting lambs are his, thus the saying that he is half of your flock. So you want to use the ram with the best qualities. Not all of the rams are going to be the best. I have some good ewes that produce better ewes when bred to a real good ram, but even then, I don't keep all the ewe lambs, I select the best, sell the rest. When selling directly to someone, I don't sell them just anything. If I wouldn't keep it for myself, I won't sell it as breeding stock to someone else. So where do all those just "ok but not exceptional" lambs go? I keep a few for my own or my meat customers, consumption. The rest go to auction.
There are buyers for livestock, cattle, sheep, goats and horses. Some places include pigs and poultry also. Buyers cannot go from farm to farm buying a few here and there, it would cover lots of miles, time and greater expense in fuel. An auction is an exchange agent, sellers bring livestock and exchange for money, buyers bring money and exchange for livestock. It may not be the very finest of accommodations, but it is the most efficient way of sellers and buyers meeting up to "exchange".
Are the animals scared? Yes. My sheep are scared right here at home when I have to run them through the chute, restrain them to trim feet, give shots, treat injuries and so on. They are scared when I load them in the trailer to take to the vet. An auction is a whole lot of scared animals. Running them through the ring makes them more scared. Cruelty is not allowed, is against the law. I know things can get wild with that many scared animals. The workers use plastic paddles to move the animals along, they do not hurt. The workers are trying to do their job with a lot of scared animals that each and every one is capable of hurting them. Some go to individual buyers that take them home to add to their own flocks. Some go to meat buyers and the animals may go to a feed lot to fatten up before slaughter.
Bottom line, you cannot keep them all. If you have several ewes, you can't even eat them all. Finding individual buyers can get difficult. You may have to steel yourself and take lambs to auction. If it is hard for you to watch, then don't. Drop them off, have the auction mail the check and go back home. You are raising meat animals. someone going to slaughter them, someone is going to eat them. They are your babies, you love them, when they leave your farm, it is no longer under your control. Your lambs are not anybody else's babies, to them they are livestock.
I've raised sheep for 10 years and have always sent the ones I was going to eat, to a slaughter facility. I've always said I could do it myself if I HAD to, but I didn't HAVE to and I paid for dropping them off as my babies and picking them up as meat. Just this month, I finally slaughtered 3 ram lambs myself. But I still couldn't shoot them, a neighbor came over and did that, then together we hung them off the tractor bucket, skinned, gutted and quartered the meat and packed it on ice. Then I took the next few days to process, vacuum seal and put in the freezer. I've processed deer, hogs, rabbits, chickens, quail and It's taken me 10 years to process my babies. So believe me, I'm not being harsh when I explain the auction process, I get it. I want the best for my babies too, but I am raising a meat animal for meat.
... As in "yields" !! 
