We develop and characterize a UV ablation technique that can be used to pattern soft materials such as polymers and nonlinear molecules self-assembled over silica microstructures. Using this method, we fabricate a spatially periodic coating of nonlinear film over a thin silica fiber taper for second harmonic generation (SHG). Experimentally, we find that the second harmonic signal produced by the taper with periodic nonlinear coating is 15 times stronger than the same taper with uniform nonlinear coating, which suggests that quasi-phase-matching is at least partially achieved in the patterned nonlinear silica taper. The same technique can also be used to spatially pattern other types of functional nanomaterials over silica microstructures with curved surfaces, as demonstrated by deposition of gold nanoparticles in patterned structures.