There are more who are really trying.
List of Muslim democracies
Wiki
The following list indicates those countries which are members of the Organization of the Islamic Conference and are either generally considered to be democratic or have substantial democratic elements in their system of government. Furthermore, the political climate in some of these countries has varied greatly in recent years, while in some of the countries there have been accusations of vote-rigging.
The percentage of Muslims in each country is sourced from CIA FactBook
Albania (Europe) (70% Muslim)
Algeria (North Africa) (99%)
Bangladesh (South Asia) (83%)
Comoros (South eastern Africa) (98%)
Indonesia (South-East Asia) (88%)
Iran (Middle-East) (98%)
Kyrgyzstan (Central Asia) (75%)
Lebanon (Middle-East) (59.7%)
Nigeria (West Africa) (50%)
Malaysia (South-East Asia) (62%)
Mali (West Africa) (90%)
Morocco (North Africa) (98.7%)
Niger (West Africa) (80%)
Senegal (West Africa) (94%)
Sierra Leone (West Africa) (60%)
Turkey (Europe / Asia) (99.8%)
Yemen (Arabian Peninsula - Asia) (+90%)
Until the recent coups d'état, Pakistan and The Gambia were also considered democracies.
Edit: I don't want to burst your bubble, but western democracy isn't perfect either.