The Brit, who plays a young Al Capone in the hit drama, is desperate for his daughter Grace, seven, and five-year-old son Alfie to see their dad on screen and has appealed to TV chiefs to allow him to be part of U.K. kids' series Bedtime Stories.
He tells London's Evening Standard newspaper, "I've always just looked for roles that I can get my teeth into. I try to bring humanity to the roles I play. I am a lot different to most of the roles I play, but put it this way - I'm never going to get offered Mr Darcy.
"My two little ones get to see very little of my work because it's a bit too much. The thing they are always watching is CBeebies, and I've been asking the BBC if I can do the Bedtime Stories slot. I keep asking them but they've never come back to me."
Stars including David Tennant, Gary Barlow and Emilia Fox have previously read on the children's show.