Science computing platforms are changing from traditional on-premises computing platforms to clouds. The style of research publications is also changing with the movement of open science. For example, it is common that researchers in the bioscience research community publish their research papers with the associated research data on the Internet. Furthermore, demands for reproducibility of computational experiments are increasing. A conventional method, or sharing source codes of application programs, is not enough to guarantee the reproducibility of computational experiments. In this paper, we propose overlay cloud architecture for building virtual clouds on cloud platforms. In the proposed architecture, the middleware, Virtual Cloud Provider (VCP), automatically configures computing environments (application programs, operating systems, libraries and binaries) that is required to reproduce computing results by using the Linux container technology. VCP also deploys containers of computing environments on clouds and configures overlay network connecting the deployed containers. A case study which considers DNA sequencing software shows how the VCP can be deployed, and used to reproduce results.