The Mining Software Repositories (MSR) field reveals knowledge for software development by analyzing data stored in repositories such as source control and bug trace systems. In order to reveal the knowledge, MSR researchers need to perform complicated procedures iteratively. To help the complex work of MSR practitioners, we study the construction of domain specific languages (DSLs) for MSR. We have conducted feature-oriented domain analysis (FODA) on MSR and developed a DSL based on the feature model. In this paper, we expand our previous work and propose to construct not a single DSL but a DSL family. A DSL family consists of a series of DSLs with commonality in their domain but suitable to specific applications of MSR. To readily construct these DSLs, we use Alloy to encode the feature model. Our encoding includes not only the DSL features and their relations but also some composition rules that can be used to generate the syntax of DSLs. Based on this, we can automatically derive the language elements to construct DSLs suitable to specific purposes of MSR.