This works as a small movement song that you can act out. Perhaps you can begin with your bird making a loud, laughing-type sounds (I say “cuckaburra” in a laughing sort of way) because the cuckaburra sounds a little like it’s laughing when it makes noise. When it flies onto a branch it can sit while keeping the beat (“Cuckaburra sits in the old gum tree”). For “merry, merry king…” I usually pulse my hands at my waist in a regal way, or you can put an imaginary crown on your head while keeping the beat. For “laugh, cuckaburra laugh…” I throw my arms in the air and pretend to laugh. You could also make your cuckaburra do something else besides laugh and have the families help to fill-in the blank.
You can also do this as a stick/sandblock song. You can use a neutral syllable to extend the activity.