Broken pull cord on my manual start Troy-bilt Pony tiller - is this an easy do-it-yourself project?

It's definitely do-it-yourself in that no special tools or skills are required, but it can be a little tricky. You can see that the the recoil starter is in an assembly which is spot welded onto a metal cover. You have to remove the entire metal cover that includes the recoil starter. There may be 6 to 10 screws to remove to do that. When you get it off you will see a plastic spool that holds the cord. This spool is probably held in place by a couple of metal tabs that are bent down. Bend those tabs up with pliers. Underneath the spool is a spiral spring that provides the recoil. Take careful note of how this all goes together. Buy a new cord (available by the foot at a hardware store) and wrap it around the plastic spool. Use a piece of tape to hold the end of the new cord above the spool so you can thread it through the hole in the metal housing later. Put the spring and the spool in place, then wind the spool to put tension on the spring - about 5 turns in the direction that would push the string out through the hole. Once you have the spring "wound up" remove the tape and thread the end of the cord through the hole. Now bend those metal tabs back down. Put the handle on the cord end (or tie a knot) to keep the spring from pulling the end of the cord back through the hole. Reassemble the rest and you are in business.