Mary, thanks for your post to my question, but the dates on his service cards differ from what you wrote.
His service cards state the following:
James Adair, Pvt, Captain John Looney's Company, 2 Reg't West Tennessee Militia, War of 1812, appears on company muster roll for Sept 20, 1814, when mustered into service, to Mch 20, 1815.Roll dated Fayetteville. Date of appointment or enlistment: Sept 20, 1814 To what time engaged or enlisted, Mch 20, 1815 (six months)
On another card is this: James Adare (same unit as above) appears on company pay roll for Sept 20, 1814 to April 23, 1815.Amount paid: 57 dollars, 25 cents.