Cut each banana in half lengthwise and halve each piece crosswise. Work with 1 wrapper at a time; cover the rest with a damp paper towel.
Lay 1 wrapper on a work surface and lightly brush the edge with beaten egg white.
Place a banana quarter 2-inches from the bottom of the wrapper and top it with 4 to 6 chocolate chips and 1 teaspoon coconut.
Fold bottom edge over filling and roll up 1 complete turn. Fold in sides and continue rolling to form a tight cylinder. Repeat with remaining ingredients.
In a medium saucepan, heat 2-inches vegetable oil to 350°. Add 2 spring rolls at a time and fry until golden brown, about 1 minute per side.
Drain on paper towels. Dust spring rolls with sugar and cocoa and serve.