Twichell's diaries are in the Beineke Library at Yale.  I've not read them
all, but what I have read shows more a chronicling of TWichell's life in
Hartford as a pastor.  There are references to Twain's performances for
the Monday Evending Club that reveal Twichell's admiration for Clemens.
(There is also some correspondence between the two that is, I think, more
revealing about Twichell's reaction to Clemens's religious struggles.)
The diaries have not been published.

        But why do you call the friendship between Twichell and Clemens
curious?  Twichell's Christianity was not fundamentalist, hidebound, or
rigid, and he was fully aware of trends in scientific and social thought.
His own faith was rather capacious and tolerant of the quests
of others. And Clemens was never SURE about what, if any, god existed, and
what, if any, consideration god might give to humanity.  He tackled these
questions energetically and regularly.   Given their mutual concern
in issues of faith, what's so curious about their friendship?

        To my knowledge, the best (still) treatment of Twichell as a
member of Clemens's Hartford community (dare I say anything about
discourse?) is Kenneth Andrews's _Nook Farm_, though I think the
qualifications I offer about the religious life of the community in
_Sentimental Twain_ are worth considering.

Gregg Camfield