If you're looking for surface markers, that would probably be a difficult question. I don't think the profile of the M2c macrophage has been well characterized on surface markers. They should produce high levels of IL-10, however. So you could do intracellular staining for IL-10. IL-4Ra surface expression has been connected with an M2c phenotype, but it's also induced in response to M1 activating signals.
As mentioned by Ashley, this is not very well-established. However, there are certain combinations of markers which might give an idea about alternative phenotype. In a recent paper from our lab, we used flow cytometry (for surface/ intracellular staining) for CD206 (mannose receptor) and arginase 1 to detect alternative activation of macrophages. We used F4/80 as macrophage markers and studies predominantly alveolar macrophages obtained by bronchoalveolar lavage (BAL). We also observed that these macrophages have reduced MHC-II expression; I am not sure whether that alone tells anything about alternative activation though. This paper also used a lot of immunoblotting analyses for different proteins following stimulation with IL-4 or IL-13.
Regulation of IL-4 Receptor Signaling by STUB1 in Lung Inflammation.