I manually updated the database as suggested.

Zen Cart 1.3.7
Patch: 1::
Database Patch Level: 1.3.7
v1.3.6 [2010-04-19 21:38:52] (Version Update 1.3.5->1.3.6)
v1.3.8 [2010-03-05 23:35:40] (Version Update 1.3.7->1.3.8)
v1.3.7 [2007-04-02 14:19:49] (Version Update 1.3.6->1.3.7)
v1.3.5 [2006-09-19 18:17:08] (Version Update 1.3.0.2->1.3.5)
v1.3.0.2 [2006-09-19 18:17:06] (Version Update 1.3.0.1->1.3.0.2)
v1.3.0.1 [2006-09-19 18:17:06] (Version Update 1.3.0->1.3.0.1)
v1.3.0 [2006-09-19 18:17:06] (Version Update 1.2.7->1.3.0)
v1.2.7 [2006-03-28 19:46:10] (Fresh Installation)

Coupon Administration now appears to work! Hooray! Thank you so much for your suggestion. I've created a test coupon and will let you know if there are any further developments. I truly appreciate your help; thanks again!