The original cornerstone of the University of the South (Sewanee
University) weighed about six tons and was made of Tennessee Pink
Marble. If it were a cube, which it probably was not, it would have
been a little more than four feet on an edge. It contained a Bible, an
Episcopal book of prayer, and other documents. It was set in a wall of
massive limestone blocks. I want to know what its dimensions probably
were, and how the hole for the documents was constructed.

This might be helpful:

Laying of the Original Sacred Cornerstone:
http://www.leonidaspolk.org/Sacred%20Cornerstone%201%2024.html

Since no one else want's to tell you,hose7-ga, the normal practice is
for the stonemason to create a hole (rectangular probably) in the top
of the corner stone.
At the stone-laying ceremony, the person  - at Swanee, the bishop -
places documents in the hole - often in a water-tight container, and
the person does his little bit of stone-laying by mortaring the lid on
the hole.  Maybe that piece shown in Bobbie7-ga 's photo is this lid.
What documents:  Probably something describing the event and naming
the personages, sometimes a copy of the newspaper of the day. Why? 
How old is the tradition?  I don't know. (Oh, you said what was
there.)
I bet Swanee U. has somewhere the things that were placed in the stone
when the building destroyed in the War between the States ("Ah'm from
down there) was torn down  - or they were ceremonially included with
those place in a new corner stone.