Let $D$ be a combinatorial simplicial model category (e.g $SSet$ with the standard model structure) and let $C$ be a small simplicial category. Of course, we can consider the projective model structure on functors $[C,D]$.
Is $[C,D]$ a simplicial model category in a canonical way?
The answer is positive when the target is the category of simplicial sets. You can find a proof in Chaper VIII of Goerss-Jardine's book. Then it follows for presented combinatorial model categories in the sense of Dugger. Any combinatorial model category is presentable, i.e. Quillen equivalent to a presentable one, so the answer is also positive in general up to Quillen equivalence. This last remark does not quite answer your question in the most general case. Nevertheless I think it's true, but I can't remember any reference at this moment.
The general case is noted in A.3.3.4 in Higher topos theory. Actually it's quite easy to prove, using the characterization of simplicial model categories in terms of powers (cotensors), since the powers, fibrations, and acyclic fibrations in the projective model structure on $[C,D]$ are all pointwise.
