David,
Yes there was a navy yard in Montgomery. The giant sidewheel ironclad CSS NASHVILLE was built there along with a presumed sister ship (possibly the PHENIX) which was said to have been damaged upon launch. The NASHVILLE was built for the Confederate Navy by the firm of J. G. Montomery and A. Anderson. She was launched in 1864 and sent down the Alabama River to Mobile for completion. She never was fully armored.
I am told by locals that the yard was located on a creek, which flowed into the Alabama River, near a railroad bridge, near the foot of Coosa and Commerce Streets.
Hope this helps.
Henry Harris