This dataset includes a comprehensive set of code and analysis scripts used to explore COVID-19 vaccine discussions on Facebook, covering three main components: Stance Classification: Using the CT-BERT model, this part of the analysis automatically classifies Facebook posts into pro-vaccine or anti-vaccine stances. The dataset was initially manually annotated and then used to train and apply the CT-BERT model, resulting in four labeled subsets: UK-Anti, UK-Pro, US-Anti, and US-Pro. An attitude-level dataset is provided in Version V3. Coordinated Link Sharing Behavior Analysis: Employing the R package CooRnet, this analysis identifies coordinated link sharing behavior (CLSB) within both anti-vaccine and pro-vaccine communities in the UK and the US. The scripts detect entities involved in CLSB by analyzing time intervals between URL shares across different entities, creating coordinated networks that are then evaluated for problematic content using Google's Fact Check Explorer Tool. Structural Topic Modeling (STM): This component uses STM to uncover thematic topics in COVID-19 vaccine-related discussions on Facebook. By incorporating document-level covariates such as publication date and geographic location (UK or US), the STM script generates a range of topics and visualizes their relationships through a topic correlation network. This dataset also contains the processed data for all figures and tables referenced in the above-mentioned manuscript. The data is organized into multiple CSV files, corresponding to specific results presented in the manuscript.