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Polycarbonate-based solid polymer electrolytes (SPEs) are being intensively studied for use in all-solid-state batteries as a viable alternative to the commonly used poly(ethylene oxide)-based SPEs. Specifically, poly(trimethylene carbonate) (PTMC) and poly(epsilon-caprolactone-co-trimethylene carbonate) (P(CL-TMC)) as a well-performing copolymeric derivative represent two materials classes that so far have not been studied in potassium battery applications. Herein, we aim to close this knowledge gap by studying physical material properties of PTMC and P(CL-TMC) solid electrolytes with potassium bis(trifluoromethanesulfonyl)imide (KTFSI) as conductive salt and examine their electrochemical stability and characteristics in K-metal/K2Fe[Fe(CN)6] (KFF), as well as Fe[Fe(CN)6/K2Fe[Fe(CN)6] cell configurations. While operation of polycarbonate-based solid-state potassium batteries at temperatures as low as 40 degrees C is feasible, comparatively low discharge capacities and capacity retention were observed in comparison to polyether-based systems. For the P(CL-TMC) material, rapid degradation through depolymerization processes in direct contact with potassium metal represents a major bottleneck. With this study, we set a starting point for further materials development in alternative polymer hosts for SPE applications in potassium batteries.