The Zr-based metallic-glass coatings with micrometer-scale thicknesses are prepared by the radio-frequency magnetron-sputtering technique on silicon substrates. Using the instrumented nanoindentation technique, we have examined the dependence of their deformation behavior, especially the indentation hardness, on the strain rate and maximum indentation depth. For the shallow indentation, in which the substrate effect can be neglected, the increase of the penetration rate leads to the decrease of the hardness. This seemingly "negative" strain-rate sensitivity is actually a result of the dependence of the degree of elastic deformation on the effective strain rate. When the indentation depth is comparable to or larger than the coating thickness, the coating interface can block the shear-band propagation and promote the shear-band multiplication, resulting in enhanced ductility and a large degree of material pileup, as shown by the measurements using the atomic force microscopy (AFM).