Climate change, invasive species and human activities are currently damaging the world's coral reefs at unprecedented rates, threatening their vast biodiversity and fisheries, and reducing coastal protection. Solving this vast challenge requires scalable coral regeneration technologies that can breed climate-resilient species and accelerate the natural regrowth processes; actions that are impeded by the absence of safe and robust tools to handle the fragile coral. We investigate ReefFlex, a generative soft finger design methodology that explores a diverse space of soft fingers to produce a set of candidates capable of safely grasping fragile and geometrically heterogeneous coral in a cluttered environment. Our key insight is encoding heterogeneous grasping into a reduced set of motion primitives, creating a simplified, tractable multi-objective optimisation problem. To evaluate the method, we design a soft robot for reef rehabilitation, which grows and manipulates coral in onshore aquaculture facilities for future reef out-planting. We demonstrate ReefFlex increases both grasp success and grasp quality (disturbance resistance, positioning accuracy) and reduces in adverse events encountered during coral manipulation compared to reference designs. ReefFlex, offers a generalisable method to design soft end-effectors for complex handling and paves a pathway towards automation in previously unachievable domains like coral handling for restoration.