This is a difficult song to research, because there seem to be several songs with the same title, or very similar titles. While doing my research, I got sidetracked on some other songs which are interesting in their own right.

Allmusic.com and Wikipedia both have some information about The Gaylords.

From them I learned that the Gaylords originally consisted of
    * Don Rea
    * Burt Bonaldi (who later took the name Burt Holiday)
    * Ronnie Fredianelli (who later took the name Ron Gaylord)
The latter two also performed under the name Gaylord & Holiday.
Burt Holiday & Ron Gaylord, Jr. (son of the original member) are now performing again as The Gaylords—see their official web site.

There is also a fan's web page: http://home.earthlink.net/~v1tiger/gaylords.html

I can't find any evidence of DORMI DORMI being released as a single by "The Gaylords" as such; however "Gaylord & Holiday" did release a single of DORMI DORMI b/w TRY TO REMEMBER. I suspect this is the recording that was later included in a couple of compilation albums attributed to "The Gaylords" namely:
"Greatest Hits" AEM CD 25841, 1993
"20 Italian Songs of Love" Hallmark CD 30573, 1996
I suspect these are both out of print.

By the way, there is a recording of DORMI DORMI attributed to "The Gaylords" at YouTube. The sound quality is poor, and the person who constructed the video says it came from an LP that she bought on eBay.

BMI.com lists a song called DORMI DORMI (along with several others of the same title) attributed to: Ronald Fredianelli, Nicola Paone, and "Public Domain Writer Share" (whatever that means). It lists Rodian Music Corporation as the publisher. This must be the song you want.