I work on call for the railroad and I need undisturbed sleep when I
get off work. The railroad will not call for 10 hours after I get off.
I know there is a phone (not mobile) that exists that can be
programmed to not ring between the times one selects.  I need this
phone with a self restoring ringer to automatically enable the ringer
after the time is up.  What is the make and model of this phone and
where can I find one?

You might want to try one of these:

Olympia OL-2410
http://www.phones-n-such.com/o2410.html
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Tropez-Vtech 
http://www.glr.com/phone/2.4GHz-Cordless-Telephone.html
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AT&T 1455
http://www.discountfamilyradios.com/attintegrated.htm
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Enjoy,
Sam

The only telephones I've found that offer a Do Not Disturb feature are
phones that are designed for multi-line business key systems. I did
find an answering machine that I believe would achieve your purpose:

"Programmable Do-Not-Disturb Option turns off speaker (room monitor)
and takes message on second ring."

http://www.epinions.com/General_Electric_2_9992_626450/display_~full_specs

Another thing that you might want to consider: many phone companies
offer a "Do Not Disturb" custom-calling feature that would enable you
to use any telephone, and activate the feature as needed for the hours
you choose. A small fee is charged for this feature; sometimes if you
bundle several custom-calling features together (such as Caller ID,
Call Waiting, Call Forwarding, etc.) you can get a bargain rate on
extra features.

Here's an example:

http://www.qwest.com/pcat/for_home/product/1,1354,16_1_8,00.html

How about getting a standard cordless phone, then plug it into a timer
(like the ones to set lights to automatically go on and off).  Tell it
to turn off at the hour, no power will go to the phone, so no phone
ringy...At the 10 hour point (which you'll have to set as the "on
time") the power will be resotred to the phone, and it will ring when
calls come in.
The timer itself should be easy to find and ~$10, and I think it
should solve your problem.
Hope this helps!