Both show share a network, and today have been confirmed to share a timeslot, Tuesdays at 9. Not only that, but the highly-anticipated Agent Carter program has confirmed launch date! The show ill start airing for eight straight weeks on January 6th at the aforementioned 9 PM timeslot. Agents of S.H.I.E.L.D. will return from a three month hiatus on March 3rd. Coulson and his pals have been airing new episodes from the first half of Season 2 on a weekly basis (except for this week, when a Marvel TV Special aired in its place). If that pace is continued in the spring, the shows last three episodes would occur after Age of Ultrons release, indicating a crossover between the two, like what the show did with The Winter Solider earlier this year, could be in the cards.
I've been a big fan of S.H.I.E.L.D. this season, but I'm really looking forward to Agent Carter. After you watch the first footage from the show, I'm sure you'll totally understand why!