A discussion in a forum raised an interesting issue, and since I ended up translating material to answer it, it seems right to give it a wider currency.
Steven Ring in his chronology of Syriac history here makes the following interesting comment:
Dated Christian tomb inscriptions written in the Palmyrene Aramaic dialect were made in Palmyra, Syria. These demonstrate that Christianity probably existed in Syria before the turn of the second century AD.
A. Vööbus, Researches on the circulation of the Peshitta in the fifth century, Baltic University: Pinneberg (1948), p.56. This states:
Tatian introduced the Diatessaron in Mesopotamia after the year A.D. 172. But it must be recognized that traces of Christendom reach further back , and they go to show that in the decades before the arrival of Tatian there must have existed early Christian congregations in Osrhoene although of Jewish Christian descent.
 Traces of Christendom reach even further back. In Palmyra, inscriptions to the memory of Christians dating from the early part of the second century, A.D. 135, are to be found. Inscriptions Sémitiques de Syrie Centrale, éd. par Melchior de Vogüé (Paris 1868).
The relevant part of this book, Inscriptions sémitiques; Pt. 1. Inscriptions araméennes, is online at the Bavarian State Library here, and may be downloaded in PDF form. The inscription is #76, on p.55.
It would be useful to add a translation of what de Vogue says. Whether modern epigraphists would agree with his conclusions I cannot say, but certainly de Vogue is very careful and scholarly for his day.
Altar 1 metre high, in the Moslem cemetary. – Copied by Waddington. – Wood, II.
To He whose name is blessed for eternity. Made by Salmon, son of Nesa, son of Tsaida, son of Barak, for his safety and that of his children.
In the month of Nisan, of the year 447. (=April 135).
The proper names in this inscription are not composed of the name of any pagan deity; there is nothing to oppose the idea that they belong to Jews.
XXX pacificus, and XXX fulmen, are found in the bible. XXX sustulit (Deus) is not, but names so composed are innumerable; the form XXX (munus Dei) exists (Gen. 25:14, 1 Par. 1:30). I have spoken elsewhere of XXX, venatio or venator, which could have been borne by a Jew of the 2nd century.
So it is not impossible that the authors of the inscription and the monument were part of the Jewish emigration settled at Palmyra.
That said, I must draw attention to the two X which surround the date at the end. These are not punctuation marks; when present, this role is normally played by ivy leaves. Our inscription offers just such an example at the end of the second line. It would be impossible, I think, to offer a Greek inscription from Syria in which the X is used for this purpose. As for the semitic inscriptions discovered so far, they do not use it either, as the reader may discover by looking through this volume.
What then is the significance of this sign, or rather this symbol?
If we were in the West, the reply is simple: the letter X, because of its double role of being cruciform and the initial of the
name Christos, is used there from very early times as a Christian symbol. De Rossi, in his learned commentary on the Christian inscriptions of Carthage (Spicileg. Solmense, IV, p. 523, 530) places it in the first rank of symbols which, before the 4th century, were used by Christians to conceal the cult of the Cross; he has collected very numerous examples from the catacombs, traces on funerary marbles, on the lime which seals tombs, and on the walls of sepulchral chambers. Was it the same in the East? There is no direct proof to authorise us to say so, but the answer is obviously yes. So far no Christian catacomb before the 4th century, no Christian monument definitely authentic erected before the peace of the church, has been discovered so far in Syria. It is therefore not astonishing that material evidence is lacking. But logic furnishes us with some definite facts; the entire history of the primitive church is there to show us a permanent current running from East to West, which we can see in the oriental customs, and particularly in the use of the Greek language, the origin of titles, formulae, and Christian symbols. It is thus almost certain that the use of the symbol in the west was preceded by the use of the same symbol in the east. After Constantine, this priority applies equally to epigraphic formulae; the forms given to the cross, at the start or end of the lines of Greek inscriptions of Syria, are in advance of those in Latin epigraphy. This fact, already signalled by de Rossi, is fully illuminated by the simultaneous publication of Christian inscriptions and monuments from central Syria. So there can be no doubt that the X was employed very early in Syria as a Christian symbol; we find it on the very first monuments erected after the triumph of the church, whether isolated, as at Chaqqa, or in a monogram with I, R or MG, as on a mass of edifices of the 4th century, too numerous to cite. As for this latter monogram, XMG, whatever it may signify (doubtles Christos Michael Gabriel), its Christian character is evident; it is proven by the numerous examples which we have collected; but it is found on monuments prior to the 4th century, as in the inscription of the great tomb of Bassus at Chaqqa (Waddington, Inscr. syr. no. 2145), where nothing else makes any allusion to Christian teachings. So we see, in Syria itself, an example of X used, with other letters it is true, to disguise the Christian beliefs of a family, i.e. to reveal it to initiates, but hiding it from those indifferent or persecutors. We may conclude, then, that even on its own, this same letter was used with a symbolic and secret sense, in Syria just as in Rome or Carthage.
From this discussion we conclude that our inscription could be Christian. If there were Christians at Palmyra in the 2nd century, they were certainly part of the Jewish community; the proper names could be Jewish; the final symbol can only be Christian, and as for religious formulae, although borrowed from the local pagan ritual, they are perfectly orthodox; the first corresponds almost word for word to the invocation Sit nomen Domini benedictum, etc., and the second may also be understood as eternal safety/salvation in the Christian sense, as well as the health of the body. So all the probabilities are in favour of a Christian character for this little monument, at least in my opinion. If scholars concerned with Christian epigraphy agree, the little altar at Palmya will be the most ancient Christian monument known, raised in public and bearing the more or less disguised sign of the cross.