In 2013, the Falcons were tied with the Panthers for the second-smallest staff in the NFL. In 2014, they'll likely be tied for third with the Bengals, thanks to the addition of a dedicated outside linebackers coach. Per the official site, here's the entire coaching staff.
In case you're wondering, there appears to be very little correlation between size and success—gonna let you guys make the jokes here—though the Seahawks do have one of the largest coaching staffs in the NFL. The Steelers have the smallest, the Patriots are near the bottom, and so forth, however, so I wouldn't use this to bolster your arguments. It's more of an interesting look at how teams assemble coaches than a predictive tool.
It's worth noting, too, that the Falcons went through some significant turnover in their staff over the last year. Offensive line coach Mike Tice, assistant offensive line coach Wade Harman, defensive line coach Bryan Cox, assistant defensive coach Andrew Thacker and outside linebackers coach Mark Collins are all new, though Collins has been with the Falcons for years. We're all hoping the turnover will lead to a drastic improvement in performance in 2014.