One such correspondent of particular interest is Lord Acton. A selection of Acton’s correspondence with Newman is available digitally courtesy of the Online Library of Liberty. Lord Acton’s periodical, The Rambler, is also the subject of seven separate files of Newman’s correspondence “concerned with various specific issues,” according to the checklist available from the national archives (PDF).
More information on the digitization project is available from the National Institute for Newman Studies, and project updates are available here.
For more on liberalism and the Catholic Church in the nineteenth century, see The Acton-Newman Relations: The Dilemma of Christian Liberalism, by Hugh A. MacDougall (Fordham University Press, 1962).