The children of that time usually wore shorter versions of their parent's clothing. To create a girl's costume from that era, you will need a dress with a full skirt that comes to just below the knees and a fitted bodice. Add fullness to the skirt with petticoats. A pair of pantaloons can be made by adding lace to the edges of a pair of cut-off white leggings. Make a frilly bonnet by trimming the back brim from a straw hat and decorating with lace and ribbons.
A young gentleman would wear a dark suit with a short coat and a pair of pants that came to just below the knees. Wear with a white shirt and either a lace collar or a bow tie. Finish with knee socks, high-top boots and a flat-brim hat.
The pioneers who settled the plains and the land across the Mississippi had to dress with a bit more practicality. For a boy, start with a pair of high-waist dress pants. Wear with a button-down shirt, buttoned all the way to the neck, and plain suspenders. These were usually in bland colors such as gray, brown and black. You will need a wide-brimmed felt hat to protect from the sun a and a pair of sturdy boots.
For a girl, wear a long print skirt with a white or matching high-neck blouse. Add a white half-apron that is almost as long as the skirt. An apron made for an adult will work. Wear with dark stockings and high-top shoes. A cloth bonnet is easy to make and a pattern can be found online.
Both cowboys and cowgirls can wear a button down shirt in checks or a solid color, a cowboy hat in either felt or straw, and boots. Boys can wear with baggy jeans and girls can wear a split skirt or a baggy pair of knee-length pants. A vest and a good pair of gloves complete the costume.
Indian costumes can be made by decorating tan t-shirts with Native American themed trim, beads and fabric paint. Use an oversize t-shirt that comes past the knees for a girl and pair the boy's shirt with tan pajama pants. Cut fringe into the sleeves and hemline. Wear moccasins and a strip of trim around the head as a headband.