A method for providing an anti-coking coating system on a surface at elevated temperatures when contacted by a hydrocarbon fluid, for example, a surface of an interior fuel passage within a fuel nozzle of a type utilized in gas turbine engines, is disclosed. The surface of the passage is rough as a result of the passage being part of a component manufactured by an additive manufacturing (AM) process. In addition, the passage may have a complex geometry of a type that can be fabricated with AM processes, for example, geometries comprising combinations of sharp bends and narrow cross-sections. The coating system comprises at least one ceramic barrier layer and an outermost metallic layer, each of which is formed using a conformal vapor deposition process.