I just got a thesis by Stig Ragnvald Froyshov entitled "L'Horologe Georgien du Sinaiticus Ibericus 34", The Georgian Horologion of Sinaiticus Ibericus 34. It's a publication of the Horologion as preserved in the 10th c. Georgian ms Sin 34 with accompanying translation in French and extensive commentaries by Froyshov.

There's a part directly related to the koinonikon. According to the Georgian ms the verses which were recited before the communion (cf. modern koinonika) are as follows:


Then there are other things following, but they aren't indespensable for our purposes.

The verses above are possibly abbreviated and maybe also the Allelouia is left out after some verses for brevity as it is usual in old mss, but it's obvious that the hymn which is strikingly similar to the koinonikon of Pascha has Allelouia. This I guess resolves the issue.

I had a look at the Typikon of the Church of Greece. There is a footnote saying that Soma Xristou is not a psalmic verse and therefore shouldn't have alleluia. They say the same for the koinwnikon of Mesopentecoste (although all musical manuscripts have Alleluia). But they don't apply the rule to the Koinwnikon of Theophany as well. What confusion..

After all my conclusion seems to be that all koinonika have alleluia and  we should chant it. Soma Xristou has alleluia but we may not chant  it to signify in yet another way the difference of the great feast (exactly as we omit other things on that day) and to respect the classical compositions (I felt bad appending an Alleluia to Daniel's Soma Xristou last time).

From the above, it is clear that in pronciple the Koinonikon is a psalmic verse with refrain "Alleluia". Only few exceptions exist: Two Koinonika are not psalmic verses but from the New Testament ("Epefanh h xaris..", "O trwgwn mou tin sarka..") but these are very close in style to the psalms.

Two other Koinwnika are more different in that they are hymnological compositions ("Tou Deipnou sou.." and "Soma Christou").  The first is a full troparion and its use on Great Thursday is special as it also replaces the Cherubic Hymn, the "Eidomen" and  the "Plerothetw".

"Soma Christou" is clearly a communion hymn, obviously ancient, short and compact and it has the form of an ephymnion (refrain).  Undoubtedly it was written for this special use like other ancient hymns which are now unused.

The use of Alleluia as a cadence of psalmic verses is general practice. Does this rule apply to the Koinonika which are not psalmic verses? For the first two ("Epefanh h xaris" and "O trwgwn mou tin sarkan") there is no doubt. They are followed by Alleluia. Although not psalmic verses, they are scriptural verses. About "Tou Deipnou sou" there is also no doubt. It is not followed by Alleluia. This hymn is all special, it was not written originally as a Koinonikon, like other ancient Koinonika which are not followed by Alleluia.

What about "Soma Xristou"? If it doesn't have Alleluia, it would be the only exception in Koinonika. This already reduces the chance for the omission to be correct but doesn't prove it.  The proponents of the omission of Alleluia argue that "Soma Xristou" is not a psalmic verse but ignore that the two other non-psalmic verse Koinonika do have Alleluia, as do a few other non-psalmic verses in our worship namely "Osoi eis Xriston", "Soson Hmas Yie Theou", the even-numbered Oikoi of the Akathistos and others.

In the Divine Liturgy, Alleluia is used in four symbolic parts of the service. In the small entrance (preparing it), preparing the Gospel reading (Alleluarion), preparing the great entrance (Chrubic hymn) and finally preparing communion (Koinonikon and "Plerothetw"). 

Our question could be anwered by ancient Typika or Pentecostaria. Unfortunately in a couple of dozen ancient and modern ones that we checked , only the beginning of the verse is given "Soma Xristou Metalavete" and not the end. Only the more modern Typikon of Dionysiou Monastery (Mt Athos) says in that margin "At the end of that, Alleluia is not chanted". Contrary to that, Xeropotamou Monastery (Mt Athos) Typikon has the whole of "Soma Xristou" verse with the Alleluia. Both of these manuscripts were written in the 19th century. Looks like it was then when this issue manifested so that the authors of Typika started to explicitly prescribe "Alleluia" or not.  The fact all previoues ones don't say anything there is a srtong argument that "Soma Xristou" followed the usual practice, that is, Alleluia was chanted after it.  This is verified by the manuscript and printed music books as well. The old manuscripts have "Alleluia", the newer publications don't.

In paragraph 43 of the the Preface of the Typikon of the Great Church (by G. Biolakis) we will find the solution to the question whether Alleluia is a sorrowful hymn and is not suitable as a scripture Alleluiarion or as a Koinonikon ephymnion in Pascha. In one place, the Koinonikon is not mentioned as a place to omit Alleluia, but in the paragraph about the Epistle reading Alleluiarion is also mentioned the Koinonikon as a place to omit Alleluia. The Typikon itself prescribes "Soma Xristou Metalabete" in the rubrics for Pascha, not specifying explicitly the omission (and obviously meaning to follow the general rule).  Although the attempt to omit the Alleluia of the Epistle failed so far, the Koinonikon did not escape the "correction".  It is though strange that the supporters of the "correction" did not extend their "corrective mania" to the ressurectional ephmnion of the second Antiphonon and the Paschal Eisodikon ("Swson hmas Yie Theou, o anastas ek nekrwn, psallontas soi Alleluia").