According to the 1860 Joseph (Sr.) and wife Mary are living in Barbour Co AL and have a son Joseph (Jr.) who was born in 1844 (+/-), well within range for enlistment. Using the NPS Soldier and Sailor listing, there are two Josephs with AL units - one with the 12th AL Infantry and Joseph L. with the 11th AL Infantry. This would be my guess. Others might be able to verify that these are your men. Good luck!