Marvel TV chief Jeph Loeb has said that Marvel can’t actually order a TV special without knowing ahead of time where it would air, so there are definitely details that would need to be worked out before we could get Peggy back in any era, Civil Rights or otherwise.
Unfortunately, we’ll probably never get a full batch of episodes with Peggy in the Civil Rights Movement, but it’s not inconceivable that we could check in with her.
Hayley Atwell has said that Peggy’s canonical long life in the Marvel Cinematic Universe means that Peggy could get back in the action at any point in any era, and she has pitched the possibility of TV specials for Peggy and Co. in the future.