Jerry, looks like you could make up a program with only Cuckoo songs. In addition to the one in the DT, there are:
The Cuckoo
Now the Sun is in the west,
Sinking behind the trees,
And the cuckoo, welcome guest,
Gently woos the evening breeze.
Cuckoo! Cuckoo! Cuckoo! Cuckoo!
Gently woos the evening breeze.
Etc. and so forth

Cuckoo Song
Oh, hear the cuckoo call,
Oh, hear him calling now!
Cuckoo! Cuckoo!
I hear your call, I hear your call,
Hear the cuckoo call.
Oh hear, how he's calling now!
and so forth

And the Ballad Index mentions the original of the one in the DT (I think, used by Lomax and Ritchie) as being recorded by Herd in 1769. (The cuckoo is a pretty bird, She sings as she flies (see verse 4 of The Cuckoo 4 in the DT).
I'm sure that there are many others. OH-OH!! I just heard a shot! Poor Cuckoo!