Serenity non-spoiler

Lis bought the book that has the shooting script in it. In a line of dialogue cut from the movie, a character says that "If we make a direct run within the hour, we're only 367,442 miles out. At full burn, we'd reach him inside of four hours."

That's referring to the title ship.

So: assume that that means max acceleration to the halfway point, then max deceleration to their goal. That means that they'll go 183,721 miles in two hours, for an average velocity of 91,861 miles per hour. Figuring that they're starting at 0 mph, they're going to hit 91,861 mph at the one-hour mark, meaning that their acceleration is 91,861 miles per hour per hour.

In order to convert that to Gs, I just plug it into the handy-dandy Google calculator, and find out that (91 861 miles) per (hour squared) = 1.16319996 g

So, the acceleration of a Firefly-class transport is about 1.16 g's.