The shipyard doesn't matter directly; the only BP the shipyard has directly is its modification rate (for increasing tonnage etc.) Ship construction times depend completely on the ship, tech, and governor modifiers. If you build a 1000 ton FAC in a 100,000 ton naval shipyard, the construction will take the same amount of time as if you built the FAC in a 1000 ton shipyard.
Only the tonnage of the DESIGN affects the annual build rate. The slip has nothing to do with it.
http://aurorawiki.pentarch.org/index.php?title=Shipyards#ShipbuildingThe shipbuilding rate is:
Normal shipbuilding rate x (1+(((Class Size / 100) - 1)/2))
So for a 10,000 ton ship, with a build rate technology of 560 bp, you would have
560 *(1+(((200/100)-1)/2))
560 * 1.5
840 ABR.
You would get this build rate, times governor bonuses, no matter what variant the ship is and no matter what size shipyard it is in.
It does not matter what the shipyard is tooled to, the tooling only determines what ships are valid to build at the shipyard and has no impact on build rates at all.