The We Need to Talk About Kevin actor covered Delmore Brothers' 'Gonna Lay Down My Old Guitar' with Tom Brosseau and Ray Price's 'I'll Be There (If Ever You Want Me)' with Becky Johns, reports AOL Music.
White contributed to the records by playing the drums and producing both singles, available digitally and on 7" vinyl records.
Reilly previously said that he prefers to act on stage rather than in movies.
"Doing theatre is a really empowering thing for an actor," he explained. "Film, as much as I love it, is a director's medium. It's not an actor's medium.
"You provide the raw materials and then the director turns it into something. Theatre is just you and the audience."
Watch the trailer for We Need to Talk About Kevin below: