As far as I can tell, the transliteration is this:
Shir hama’alot l’David samachti b’omrim li bet Adonai nelech
Om’dot hayu ragleinu bisharayich Y’rushalaim
Y’rushalaim habenuya k’ir shechubra-lah yachdav
Shesham alu sh’vatim shivtei-yah edut l’yisrael l’hodot l’shem Adonai
Ki shamah yashvu khisot l’mishpat kisot l’veit David
Sha’alu sh’lom y’rushalaim yishlayu ohavayich
Y’hi-shalom b’cheilech shalvah b’arm’notayich
L’ma’an-achai v’re’ai adabrah-na shalom bach
L’ma’an beit-Adonai eloheinu avakshah tov lach
I haven't studied Hebrew extensively, but I learned the alphabet a while back and used several resources to transliterate, including:
http://www.levsoftware.com/Vmain.htm
http://en.wikipedia.org/wiki/Niqqud
http://en.wikipedia.org/wiki/Hebrew_alphabet
http://www.biblegateway.com/passage/?search=psalm%20122&version=WLC
Here is a recording of the passage (Psalm 122) being read aloud by a native speaker:
http://www.aoal.org/Hebrew/AudioBible/27_Psalms/27-Psa_122.mp3
Enjoy! I hope it is accurate enough for your piece. Anyone reading this who has more knowledge of Hebrew than I do, please feel free to correct this.