Off-the-shelf large language models (LLMs) are increasingly used to automate text annotation, yet their effectiveness remains underexplored for underrepresented languages and specialized domains where the class definition requires subtle expert understanding. We investigate LLM-based annotation for a novel legal NLP task: identifying the presence and sentiment of credibility assessments in asylum decision texts. We introduce RAB-Cred, a Danish text classification dataset featuring high-quality, expert annotations and valuable metadata such as annotator confidence and asylum case outcome. We benchmark 21 open-weight models and 30 system-user prompt combinations for this task, and systematically evaluate the effect of model and prompt choice for zero-shot and few-shot classification. We zoom in on the errors made by top-performing models and prompts, investigating error consistency across LLMs, inter-class confusion, correlation with human confidence and sample-wise difficulty and severity of LLM mistakes. Our results confirm the potential of LLMs for cost-effective labeling of asylum decisions, but highlight the imperfect and inconsistent nature of LLM annotators, and the need to look beyond the predictions of a single, arbitrarily chosen model. The RAB-Cred dataset and code are available at https://github.com/glhr/RAB-Cred