If your child needs a little more movement than simply putting the shamrocks on the table, then you could also tape the shamrocks (sticker side down) on the wall. Have your child throw a bean bag at the wall. Whichever shamrock he/she hits (or is close to hitting), let him/her pick that shamrock. That can make the same game seem very different to a child.
If you have access to ellison cuts (dye-cuts) at a school, then cutting out shamrocks using the dye-cut would be a lot faster! I laminated mine to help with durability.