This is not my best-researched effort (which likely says a lot). According to Wikipedia, which provides a transliteration, Cyrus Gordon published this inscription (and transliteration) in Evidence for the Minoan Language (1966). I have been unable to find serious subsequent decipherment attempts - although I haven't in earnest started amassing evidence for a literature review. Taking the account at face value - and in light of the bilinguality of this inscription from Amathus, I would like to offer my own explanation of the inscription as either West Semitic or specifically Canaanite (this depends on the interpretation of the vowel /o/ as an aleph (i.e. Canaanite) or just another transcription of /u/ - which is the basis of my first attempt):
3: Η ПΟΛΙΣ Η АΜАΘΟΥΣΙΩΝ ΑΡΙΣΤΩΝΑ
4: ΑΡΙΣΤΩΝΑΚΤΟΣ ΕΥΠΑΤΡΙΔΗΝ
Cyrus Gordon translates this text as
The city of the Amathusans (honored) the noble Ariston (son) of Aristonax."
So in light of that Greek inscription/translation (I have reformatted/re-parsed the syllabic transliteration but I have also taken it from Wikipedia):
1: a-na ma-to-ri U-mi E-s[a]-i mu-ku-la-i . la sa-na A-ri-si-to-no se A-ra-to-wa-na-ka so-ko-o . se
2: ke-ra-ke-re tu-lo . se ta-ka-na-[?]-so-ti a-lo-ka . i-li-po-ti
Ana matori Umi Esa'i mukula'i . La sana Arisitono se Ara(s)towanaka sokō . se
keraker tulo . se takana[?]soti aloka . ili-poti
"To the small boat of Um-Hasa the mooring point, for the Second Ariston of the regal Ara(s)towanaka. This is the
'hanging talent' [of gold]. This is my tribute to you. Ili-Puti."
Then Amathus would actually be a corruption of Um-Hasa; really probably Um-Hatha. The occurrences of /o/ are interesting - mator (Akkadian maturru), Aristono (Greek Ariston); Aratowanaka (Greek Aristonax), soko'o (Akkadian sukkû from Elamite sunki-), tulo (Akkadian tullû); Ili-Poti (probably Ili-Puti (the second part of the compound frequently found with gods in Akkadian)). The only outlying orthography would then be aloka (which I take as a form of 'lyk - found in Hebrew, Aramaic, and Arabic) - and the reason for this vowel may simply be a vowel interchange issue in which /ei/ interchanged with /o/ so that 'aleyka becomes aloka.
So two possible conclusions: The dialect 'heard' and approximated /o/ from (Standard? or Neo-?)Babylonian u and from Greek o. It is also possible (if not likely) that the first sentence's inflection is anomalous and the dialect also did not possess inflection. The first sentence, complete with Akkadian preposition, would then be an attempt to employ a very formal (archaic) language, namely (probably) Akkadian. And the balance of the text simply ignores this inflection.
Nobody's ever actually posted a question, but preemptively, my interpretation of mukula comes from the Akkadian makallû a Standard and Neo Babylonian word for "mooring place." Exactly why this would be the chosen term to describe Amathus is unclear. It could, however, have been the dialect's chosen word for a coastal city, inasmuch as the juxtaposed Greek word is polis. However, CAD connects the verb kalû really 'to detain.' I wonder if it isn't a related but slightly different term for coastal (or non-river) city from mu 'water' and kula 'detained' - possibly meaning either 'shallow water' (i.e. mooring place), or a place 'denied water' (kalû can specifically mean 'to deny irrigation water').