We colored on regular old copy paper. You should color hard, making the colors very dark so there is a nice thick layer of wax on the paper. Then blow off the excess bits of wax, turn the paper over.
I remember putting a couple layers of newsprint or copy paper down on the ironing board, then the fabric, then the colored paper (face down), then another piece or 2 of paper, then the hot iron. Now that you mention it, I do remember pressing long and hard -- even scorching some of the paper a bit (but not the fabric).
A couple of times, we pulled the paper up only to find that it was not yet dark enough. After a couple of "test" presses, however, we figured out how much pressure and time it took and it went smoothly after that.
Remember -- the more wax you put onto the paper, the more color there is to sink into the fabric. If it is too light, try more crayon. If the child doesn't have the patience to color that hard or long on the project, maybe you could go over her work. Because it will be her design and her colors, she will probably never even notice.
Good luck.
BethMI