We study the light quark mass dependence of the D and Ds meson decay constants, fD and fDs, using a covariant formulation of chiral perturbation theory (χPT) at next-to-next-to-leading order (NNLO). Using the HPQCD lattice results for the D (Ds) decay constants as a benchmark we show that covariant χPT can describe the HPQCD results better than heavy meson χPT (HMχPT) at both NLO and NNLO. Within the same framework, taking into account sub-leading (1/mQ, with mQ the heavy quark mass) corrections to the values of the low-energy constants and employing the lattice QCD results for gBB⁎π, we estimate the ratio of fBs/fB to be 1.22−0.04+0.05, which agrees well with the HPQCD result 1.226(26).