Here is a cool website that has a ton of recipes that you can try.
http://www.drinksmixer.com
The following is the standard recipe for a fruit flavored Daiquiri. For a Midori Daiquiri substitute 1 oz Midori for 1 oz (any type of fruit flavored liqueur)
Fruit Flavored Daiquiri
1 oz (any type of fruit flavored liqueur)
1/2 oz Light Rum
1 1/2 oz Lemon Mix
Shake with ice and strain into a cocktail glass.
See this site for Midori recipes:
http://www.midoriworld.com/recipe1999.html
Frozen Midori Daiquiri
1 oz. (30 ml.) Midori
1 1/2 oz. (45 ml.) Light Rum
1 oz. (30 ml.) Sweet & Sour Mix
1 oz. (30 ml.) Lime juice
*Combine ingredients in blender with 1 cup crushed ice
*Blend until smooth