more like "musslim" or "muslim" where the 'u' and the 'i' are pronounced relatively weakly. but depends on where the word is pronounced (arabic words' sound changes when becomes single/plural/male/female etc...) you can be sure (to the best of my knowledge) the 'z' in 'muz-lim' is wrong (unless someone can give me an arabic example that I have overlooked).

Mos-lim A Muslim (Arabic: مسلم‎) is an adherent of the religion of Islam. The feminine form of 'Muslim' is Muslimah (Arabic: مسلمة‎). Literally, the word means "one who submits to God". The word "Muslim" is the participle of the same verb of which "Islam" is the infinitive.[1] Muslims believe that there is only one God, translated in Arabic as Allah. Muslims believe that Islam existed long before Muhammad and that the religion had evolved with time from the time of Adam till the time of Muhammad, and was completed with the revelation of verse 3 of Surah Al-Maeda "This day have I perfected your religion for you, completed My favour upon you, and have chosen for you Islam as your religion." The Qur'an describes many Biblical prophets and messengers as Muslim: Adam, Noah (Arabic: Nuh), Moses (Arabic: Musa) and Jesus (Arabic: Isa) and his apostles. The Qur'an states that these men were Muslims because they submitted to God, preached his message and upheld his values. Thus, in Surah 3:52 of the Qur'an, Jesus’ disciples tell Jesus: "do thou bear witness that we are Muslims". Muslims pray five times a day; these five prayers are known as Fajr, Zuhr, Asr, Maghrib, Isha. There is also a special Friday prayer called Jumu'ah. Currently, the number of Muslims is estimated to be 1.3 billion. http://en.wikipedia.org/wiki/Muslim

pronunciations are a little difficult to convey accurately in print. You're very much closer with your second option. I would say it's Muss-lim with the 'muss' bit following the vocal pattern of 'push' While we're at it Islam is not iz-lum, as rendedred by many who know not, but it is iss-laam.