The increasing ubiquity of GPUs is accompanied by the increasing complexity of their hardware and parallel programming frameworks. Directive-based parallel programming standards like OpenACC simplify GPU programming to some extent by abstracting away low-level complexities, but a fair amount of expertise is still required in order to use those directives effectively. We introduce ACCeLLiuM, two open weights Large Language Models specifically fine-tuned for generating expert OpenACC directives for data-parallel loops, along with the supervised fine-tuning dataset that was used to train them. The ACCeLLiuM SFT dataset contains 4,033 OpenACC pragma-loop pairs mined from public GitHub C/C++ repositories, with 3,223 pairs for training and 810 for testing. Experimental evaluations show a pronounced performance gap in generating correct OpenACC pragmas between base LLMs and our fine-tuned versions. On the held-out test set, base LLMs fail to consistently generate valid pragmas, whereas LLMs fine-tuned on the ACCeLLiuM dataset generate valid pragmas with the correct directive type for $87\%$ of the data-parallel loops, and exact pragmas--including directives, clauses, clause order, and clause variables--for $50\%$ of the cases. Even when not exact, generated pragmas frequently incorporate the correct clauses in a different order than the ground-truth label, or include additional clauses that enable finer control over parallel execution, data movement, and concurrency, offering practical value beyond strict string-matching. By publicly releasing the code, models, and dataset as ACCeLLiuM we hope to establish a reproducible benchmark for LLM-powered OpenACC pragma generation, and lower the barrier to automated GPU offloading of serially written programs.