The most detailed book available for studying ordnance of Illinois regiments is "Arming the Suckers" by Ken Bauman. It lists quarterly ordnance reports for virtually every Illinois regiment during the war, usually beginning in late 1862 or early 1863 and running through the war.
The 61st Illinois Infantry was armed primarily with Austrian rifle muskets throghout all of 1863 into early 1864, with some Enfields also being issued. Beginning with the second qtr. of 1864, U.S rifle muskets began to dominate the regiment's small arms, with some Austrians and Enfields also still being present.