We studied the selective deposition of a Newtonian liquid on the hydrophilic domains of chemically patterned substrates. We present experiments and numerical simulations of the dip-coating and self-metered die-coating of compact, geometrically convex patterns such as squares and diamonds. The coating of such patterns is intrinsically an instationary process. Nevertheless, the maximum film thickness entrained on diamonds that are either much smaller or larger than the lengthscale governing the coating process follows the theoretical predictions derived for steady-state coating of either narrow hydrophilic stripes or chemically homogeneous surfaces. The transition between these two regimes is determined by the ratio of the pattern dimensions and the characteristic length of the reservoir meniscus, i.e. the capillary length for dip-coating and the die-gap for die-coating processes. While the film thickness entrained on diamonds scales with the coating speed as a powerlaw, the entrained thickness on squares with sides oriented parallel and perpendicular to the coating direction appears to saturate for small coating speeds. This influence of the azimuthal pattern orientation is related to the capillary break-up of the coating meniscus. Residual satellite droplets observed underneath the hydrophilic patterns after coating are a consequence either of the break-up or the subsequent retraction of the coating meniscus.