If they have alot of them on their farm ( I'm in the same situation) then they are going to be more prevalent in certain areas, and even follow a pretty set routine sometimes.
First off, they like water. Alot. If there is any standing water, creek, stock tanks, etc. start in that area and look for food sources nearby. If they can, they like to wash their food. ( if you ever find an outdoor pet's water dish extremely dirty, and it seems to have gotten that way overnight, guess what visited). They like cover also. They seem to be more bold all the time towards people, and coming out during the day etc. but they still like to have a place to hide. Drainage pipes that are dry or mostly dry for fairly long intervals are common ways for a coon to get from point A to B. If their is a stand of trees at one opening and a feild of sweet corn at the other end, they can go back and forth as they please and sometimes have a source of water to boot. It also makes an excellent place for a trap or ambush.
Pay attention to the ground also, coons can be so set in their ways you wouldn't beleive it. Its not uncommon at all for them to follow the same path in and out of the woods, or to cross a fence at one spot every time. They'll do it so often they kill the grass. If you see what looks like a path worn in the grass, or at least where the grass is smashed down. You know something was there more than once, and if you have a raccoon problem theres a good chance thats what it was.
Your best bet for hunting them without a dog, is to let them come to you. Position yourself in an area where they're very likely to be, food, water and cover all close together, or if there are several spots, walk quietly back and forth, hit each spot about every half hour or so. If you find a path, thats a good place to check out too. They're very easy to trap once you understand them, and have their behavior in the area patterned. I think that might be more successful than hunting, but both should do fine, and if you hunt you dn't have to clen the dang trap out. They pull everything they can get their paws on into the trap once they're caught and nothing short of a pressure washer seems to work well at getting it all back out.