We are certainly not the first and won't be the last to create a train out of a diaper box. In fact, my nephew was also an engineer in a diaper box engine this year and my sister and I both arrived at the idea without talking to each other. There are a large variety of ways people have made this kind of train and I read many of them. Then, as usual, Patrick and I kind of made it up as we went.
We used the parts we cut out to finish it all up. I added a front panel to the back part after taking this picture. Also, note that we used a Styrofoam cup because that is what we had on hand. Paper or plastic would have been much preferred as the spray paint melted the cup slightly. After taking this picture, we also attached a pilot (the grill thing) to the front of the train.
We decided to use 3 colors for our train, gold metallic, flat black, and satin red. I went through a very lengthy process of painting in layers, much like a printing press.
I made good use of my temporary spray adhesive that I purchased for my wall art to make paper stencils to cover each layer. I even used a straight edge to make custom width tape for all the stripes and the pilot's grill. It worked quite well, though not perfectly; there are spots were paint got under the stencils. We sprayed the wheels separately, and hot glued then on at the end.
We finally attached some straps to keep it up and added a bike light to the front by cutting a hole. We put some stuffing that we sprayed lightly with some black spray paint into the funnel. Then we inserted one Peter to drastically increase the adorableness.