Collin,
first question: are looking for these liturgies and resources for the Melkite Greek Catholic Church or the Antiochian Orthodox Church or (for the Greek only) the Greek Orthodox Church? If you're interested in Greek Orthodox texts in Greek or Byzantine texts in English--and don't care about a particular translation--there are tonnes of resources out on the Internet.
The Greek Orthodox Church in the US has a good choice of liturgical texts on line, in Greek and English. Some samples of Greek Byzantine chant also available there. See here, i.a.:
http://www.goarch.org/en/chapel/text.asp.If you're interested in Melkite liturgical texts, PM me with your e-mail address and I can forward you some. I only have them in Arabic and English. I do not have anything at all in transliterated Arabic (i.e., so people who cannot read Arabic can pronounce it). If you have a particular prayer or troparion or similar that you wish transliterated, let me know.
The Melkite eparchy in Canada has some nice videos and music of the Divine Liturgy sung in Arabic and Greek (e.g.
http://www.melkite.com/chant/index.html). Some of these and similar ones have been posted on YouTube.
The Melkite eparchy in the US has texts in English for sale:
http://www.melkite.org/SophiaPress/sophia_press_orderform.htm . I'm not aware of them having anything in a transliterated Arabic, although they may. The patriarchate in Damascus and the Melkite Paulists have the texts in Arabic (no transliteration), some in English, and some in French.
Lastly, try Abouna Samir's site:
http://www.rannem.com/ . (The Arabic word "rannama" means 'to chant'.) There are some recordings of music from the Nativity, Great Lent, Easter, as well as some general hymns--all in Arabic. (Although Sr Mary Keyrouz sings partly in Greek as well.)