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?



Is the projective model structure simplicial?
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.


