The BICEP/ Keck series of experiments target the cosmic microwave background at degree-scale resolution from the South Pole. Over the next few years, the “Stage-3” BICEP Array (BA) telescope will improve the program’s frequency coverage and sensitivity to primordial B-mode polarization by an order of magnitude. The first receiver in the array, BA1, began observing at 30/40 GHz in early 2020. The next two receivers, BA2 and BA3, are currently being assembled and will map the southern sky at frequencies ranging from 95 to 150 GHz. Common to all BA receivers is a refractive, on-axis, cryogenic optical design that focuses microwave radiation onto a focal plane populated with antenna-coupled bolometers. High-performance antireflective coatings up to 760 mm in aperture are needed for each element in the optical chain, and must withstand repeated thermal cycles down to 4 K. Here, we present the design and fabrication of the 30/40 GHz anti-reflection coatings for the recently deployed BA1 receiver, with indices matched to its various polyethylene, nylon and alumina optical components. We describe an epoxy coating technique designed for alumina optics, which achieves better than 80% transmission at room temperature. For polyethylene optical elements, we present a new heat-compression approach that allows low-density polytetrafluoroethylene AR layers to reach sub-percent reflected power. We describe the planned use of these methods for the next BA cryostats, which may inform technological choices for future small-aperture telescopes of the CMB-S4 experiment.