Good quality Rhode Island Reds (not hatchery) are a deep, almost mahogany red in color. Maybe that would be a good place to start? Good luck with your project!

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My New Hampshire cockerel certainly a bright red orange, but super human aggressive, so he ended up in the freezer.Show quality New Hampshire reds are the closest I can think of. Though, compared to a cardinal, they’re more orange.
thanksSomeone posted a link recently where everyone showed off their favourite fancy birds. I recall one member had some outstanding birds.. in the most remarkable mahogany's and reds. But yeh.. the red of a cardinal.. that would be a very tough objective.