Help identifying and locating a Greek song

I am looking to find a song my father and I would sing when I was a kid.
The name of the song as he spoke it to me was Kelithista or Kelivista. Pronounced Keh-Lie-Thee-Stah
It's an old Greek love poem/song about a man who talks to a bird about his love for his girlfriend (or something like that).
He told me the translation was something like "little birdie".

Anyways, here is the EXTREMELY butchered attempt at writing the words as I remember them.

Kelithista Oh Rea Pumalikya Kelithista.
Kelithista Travuthista. Kelthista Travuthista.
Esteeneah Esteeneah Guabapo.

Then the next stanza was something like.

Ahnie Parkie...

I'm looking for this song to play at his memorial so any help would be greatly appreciated.

Thanks!
Demetre

Ps. Since you recently joined ATL... Wellcome Δημήτρη!

Thank you so much! That was exactly it!