Black box deep learning models trained on genomic sequences excel at predicting the outcomes of different gene regulatory mechanisms. Therefore, interpreting these models may provide novel insights into the underlying biology, supporting downstream biomedical applications. Due to their complexity, interpretable surrogate models can only be built for local explanations (e.g., a single instance). However, accomplishing this requires generating a dataset in the neighborhood of the input, which must maintain syntactic similarity to the original data while introducing semantic variability in the model's predictions. This task is challenging due to the complex sequence-to-function relationship of DNA. We propose using Genetic Programming to generate datasets by evolving perturbations in sequences that contribute to their semantic diversity. Our custom, domain-guided individual representation effectively constrains syntactic similarity, and we provide two alternative fitness functions that promote diversity with no computational effort. Applied to the RNA splicing domain, our approach quickly achieves good diversity and significantly outperforms a random baseline in exploring the search space, as shown by our proof-of-concept, short RNA sequence. Furthermore, we assess its generalizability and demonstrate scalability to larger sequences, resulting in a ~30% improvement over the baseline.