We consider inference about a scalar coefficient in a linear regression with spatially correlated errors. Recent suggestions for more robust inference require stationarity of both regressors and dependent variables for their large sample validity. This rules out many empirically relevant applications, such as difference-in-difference designs. We develop a robustified version of the SCPC method of Müller and Watson (2022a) that addresses this challenge. We find that the method has good size properties in a wide range of Monte Carlo designs that are calibrated to real-world applications, both in a pure cross-sectional setting, but also for spatially correlated panel data. We provide numerically efficient methods for computing the associated spatial-correlation robust test statistics, critical values, and confidence intervals.