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Nanodiamonds containing nitrogen-vacancy (NV) centers can serve as colloidal quantum sensors of local fields in biological and chemical environments. However, nanodiamond surfaces are challenging to modify without degrading their colloidal stability or the NV center's optical and spin properties. Here, we report a simple and general method to coat nanodiamonds with a thin emulsion layer that preserves their quantum features, enhances their colloidal stability, and provides functional groups for subsequent crosslinking and click-chemistry conjugation reactions. To demonstrate this technique, we decorate the nanodiamonds with combinations of carboxyl- and azide-terminated amphiphiles that enable conjugation using two different strategies. We study the effect of the emulsion layer on the NV center's spin lifetime, and we quantify the nanodiamonds' chemical sensitivity to paramagnetic ions using $T_1$ relaxometry. This general approach to nanodiamond surface functionalization will enable advances in quantum nanomedicine and biological sensing.