In a small saucepan, bring water and sugar to a boil over high heat; reduce heat to medium and simmer for 2 minutes, until slightly thickened. Let cool to room temperature. (to speed up cooling of syrup place in fridge for 40 - 45 minutes.).
Stir cooled syrop into banana puree.
Freeze in ice cream maker according to manufacturers directions.
Place in a shallow pan covered with plastic wrap for at least 4 hours.