Coy dark matter removes the tension between the traditional WIMP paradigm of dark matter and the latest exclusion bounds from direct detection experiments. In this paper we present a leptophilic coy dark matter model that, on top of explaining the spatially extended 1–5 GeV γ-ray excess detected at the galactic center, reconciles the measured anomalous magnetic moment of muon with the corresponding standard model prediction. The annihilation channel of dark matter is χχ→ττ¯ with the dark matter mass mχ=9.43(-0.52+.063stat)(±1.2sys)  GeV given by best-fit of the γ-ray excess. Fitting the measured anomalous magnetic moment of the muon requires instead a pseudoscalar mediator with a minimal mass ma=12-3+7  GeV.