Make or purchase a coyote fur hat pattern. Having a pattern from which to make a coyote fur hat is a necessity.
Gather your supplies, sewing materials, and pattern in one work area. Lay the padded hat lining material out on a table. Position the pattern pieces on top of the lining material.
Cut the padded liner material out using your hat pattern. Thread the standard-sized sewing needle with your thread. Tie a knot on one end. Stitch the padded liner material together using the office clips to hold the seams together while you stitch. After stitching all pieces of the padded hat lining together, place it on the styrofoam wig head frame so that it fits properly. Try the foam lining on your own head. The lining should not fit tightly.
Lay the coyote hide out on the table with the fur side down against the table. Position your pattern pieces on the coyote fur hide. The top skull part of the pattern should be near the top of the face of the coyote, depending on whether you want the coyote face on your hat.
Trace the pattern pieces out with a pen on the skin of the coyote hide. Try to keep the patterns lined up so the fur is going in the same direction on all pieces.
Cut along the pen lines that you drew on the coyote hide with an Exacto knife. Remove each piece of the coyote fur. Clip the top of the skull pattern oval to the first side of the pattern.
Thread the heavy duty needle with the artificial sinew and tie a knot on the end. Stitch the coyote fur side pieces to the oval skull cap part using a blanket stitch.
Fit the coyote hide hat on the styrofoam wig frame. Insert the foam lining hat inside of the coyote fur hat. Flip the coyote fur hat inside out. Clip the edges of the foam hat lining to the skin part of the coyote fur hat. Stitch the lining edges to the coyote fur hat. Test the hat for fit and style on the wig frame. Make any adjustments as needed by cutting stitches and sewing again if necessary. Try the hat on for size.