I want to be able to shoot a card of some sort (playing card or some kind of paper disc maybe) about 40-50ft and be accurate enough to have it hit within the span of a 3ft circle. I want to be able to EASILY shoot about 60 cards per minute for like ten minutes, before reloading.
Is there a product on the market that does just this? I’ve been searching and haven’t found one.
Would this be easy to make, with a spinning rubber wheel and a card loader?
Whoa, back up there pardner. Is this shooting as in with a firearm? You have a gun that can hold 600 rounds and you can shoot in once a second for 10 minutes with no problem? We had a thread on Annie Oakley a little while ago and discusses some stunts like these. Are you planning on channeling her and going on tour?
The guys on Mythbusters built one on the episodes called “Exploding Jawbreaker”. The final version was able to throw cards at up to 150mph with pretty good accuracy. It was a spinning wheel device, though you would have to view the original episode to get the details of construction.
“Don’t try this at home. We are what you call experts.” 
Oh, I think I misunderstood the OP. However, if you read carefully, my alternate interpretation is fully supported. I was trying to figure out the hows and whys of all of it all and it was pretty entertaining.