High-resolution ground penetrating radar (GPR) is a critical tool for subsurface remote sensing, but the high cost and strict size, weight, and power constraints of traditional systems limit their widespread deployment, particularly on unmanned aerial vehicles (UAVs). While software-defined radios (SDRs) offer a flexible alternative, implementing high-resolution stepped-frequency continuous-wave (SFCW) radar on low-cost SDRs introduces fundamental challenges: synthesizer phase incoherence caused by independent phase-locked loops and severe data transport bottlenecks. This article introduces the stepped-frequency coherent radar architecture (SCORA), an open-source framework designed to transform a low-cost, commercial SDR into a fully coherent SFCW radar for near-surface geophysics. The framework features built-in support for both continuous-wave (CW) and linear frequency modulated (LFM) subpulses, utilizing an extensible architecture that allows users to easily integrate custom, advanced waveforms. SCORA utilizes reference-channel compensation and incorporates system latency characterizations to optimize PRF and prevent spatial aliasing. The framework is experimentally validated through free-space ranging, sandbox landmine detection, and an airborne UAV survey that successfully mapped the buried infrastructure. This open-source release significantly reduces the barrier to entry for agile GPR instrumentation.