The recent surge of building software systems powered by Large Language Models (LLMs) has led to the development of various testing frameworks, primarily focused on treating prompt templates as the unit of testing. Despite the significant costs associated with test input execution and output assessment, the curation of optimized test suites is yet overlooked in these tools, which calls for tailored test selection or prioritization strategies. In this paper, we show that diversity-based testing techniques, such as Adaptive Random Testing (ART) with appropriate string distance metrics, can be effectively applied to the testing of prompt templates. Our proposed adaptive testing approach adjusts the conventional ART process to this context by selecting new test inputs based on scores derived from existing test suite and their labelling results. Our results, obtained using various implementations that explore several string-based distances, confirm that our approach enables the discovery of failures with reduced testing budgets and promotes the generation of more varied outputs.