My wife is in cosmetology school and paid out of pocket for an eyelash certification course. Can we claim that on our taxes (filing jointly)?

You  will have to ask the school if they are an eligible education institution. 

If they are, enter the expenses under Federal, Deductions & Credits, Scroll down to Education 

According to the IRS:

“Eligible educational institution. An eligible educational institution is any college, university, vocational school, or other postsecondary educational institution eligible to participate in a student aid program administered by the U.S. Department of Education. It includes virtually all accredited public, nonprofit, and proprietary (privately owned profit-making) postsecondary institutions.

An eligible educational institution also includes certain educational institutions located outside the United States that are eligible to participate in a student aid program administered by the U.S. Department of Education.

The educational institution should be able to tell you if it is an eligible educational institution.”