This app was mentioned in 2 comments, with an average of 5.50 upvotes
If we're talking about the physical black card, drawn from an actual CAH deck, there here's a way that would work which is not expensive:
1) Buy a Chromecast for $35; plug it into the HDMI port of the TV which will display the item, and get it set up on the local WiFi network.
2) On a smartphone or tablet you use on that same WiFi network, download and install a free app which uses a Chromecast device to project pictures up to the TV screen. One such that you could use, for example, is EZCast, which is available for both Android and for iPhone/iPad.
3) Take a photo of the black card, then project it up to the screen via Chromecast and the app (EZCast or comparable). Next black card, take another photo and then cast it again. Etc.
Simple, cheap solution, I think. I've heard of Raspberry Pi but never used one, so I don't know if that's a better solution or not. Chromecast is cheap and easy to deal with.
You know... EZCast can cast web pages without screen mirroring. But as far as cheap tablets... You'd probably be happy with the Nexus 7.