Are they ranching sheep or cattle?
Okay. As an American, "ranch" makes me think northern plains. As others have said, game, if they could get it: any number of fowl, jackrabbits, antelope, maybe even bison. Fish, during the warm months. If they're ranching cattle, they have dairy available to them: milk, buttermilk, butter, cream, cheese. I've never particularly heard of American ranchers using sheep's milk, but look into it. I assume they eat some of their own beef or mutton, though maybe only at slaughter-time. Cornmeal, made into hasty pudding or cornbread. Beans. Wheat flour would have been rarer, and would have been quite dark compared to regular white flour today. Garden vegetables, especially peas, beans, lettuce, and radishes in the springtime, tomatoes and ground-cherries in the summer, and pumpkins, peppers, squash, potatoes, onions, and cabbage in the fall/winter. Research what fruit was native to your area--I'm not familiar enough with the northern plains to rattle anything off the top of my head, though Laura Ingalls talks about plums in Minnesota.
A particularly popular dish was fricassee. Look it up. Wild rabbits need to be stewed low and slow to be worth eating. Remember that unless it's freezing outside or your people have tons of salt (which they won't,) meat has to be smoked or else eaten immediately. They won't have a ton of sugar for making preserves, either. I assume, being ranchers, their main cooking fat will be tallow.
1850s/1860s would have been before the railroads came to most of the northern plains. That means everything had to be carted out by wagon, which means there was very little commercial carting-out at all, so if your family have been on their ranch long term, you can scuttle the idea of salt pork and white flour, and tell us they tried to grow corn and beans (though if a piece of land is being ranched instead of farmed, there's a reason: it doesn't farm well.) Barbed wire wasn't invented until 1867, and until then, ranching was not as profitable a business as was afterward. Also, remember the Civil War happened 1861-1865. The northern plains weren't geographically involved in it, but the Union was preoccupied.