There are thousands of songs, which you can buy musical movements for. If you have to make (or modify) a music box to play your own song it is going to be difficult, but it can be done. You can expect to try it a few times before you get it right. In the end, you will have something completely unique and intensely personal.
Find the notes in the song you want to play. If the song is written down in musical notation, go through the composition and write down the notes. If the song is not written down, you should slowly play the song on a piano with one hand while you write down the notes with the other.
You will need a comb with all the notes of the song you want to play. You can order combs and cylinders from the same companies that sell music box movements. The cylinder is the tiny drum with pins that rotates when the song is playing. The pins on the cylinder strike the teeth of the comb in a pattern that plays the notes of the song.
Next, you need to buy a roll of music wire from a hardware store. Take in the old cylinder so you can get the music wire in the proper diameter. Cut the number of pins (one per note) that you are going to need. The pins should be about half of the diameter of the cylinder. They don't have to be exact as you can adjust them during assembly. You should take off any burrs or sharp edges with a small file of sandpaper.
Wrap a piece of paper around the cylinder and mark the places where the pins will go. Draw a series of parallel lines across the paper. The distance between the lines is going to determine how far apart the notes are. You can estimate this distance by wrapping another piece of paper around the old cylinder
Drill holes in the cylinder wall that match the notes on the paper guide. The drilled holes should be just big enough to hold the sections of music wire. Insert the pins so that they extend just far enough above the outer surface of the cylinder to hit the teeth of the comb. When all of the pins are in place, fill the inside of the cylinder with glue.
When the glue is dry, put the comb and cylinder in place and try it out. You will probably have to try to make the cylinder several times before you get it right.
You can make the music box sound a lot better if you occasionally hit more than one note at a time.
If your melody has the same note played in rapid succession it is possible that your cylinder will contact a tooth of the comb while it is still vibrating. This will produce a weak second note. If you have room on the comb, you can order it cut so that two teeth produce the same note and avoid this problem.