
Phasics |

ya Wiz
although for thematic and RP reasons you could also argue Alchemists and Witches are also good candidates for constructs since both offer very nice flavours slants on crafting constructs. Alchemical Golems etc.
but you can beat Wiz from a mechanical point of view, they also get bonus feats to make gaining those craft feats easier.

Cheapy |

In UM, there's a Arcane Discovery that lets them craft constructs without taking Craft Construct, Craft Wonderous Items, or Craft Magical Arms and Armor. It only applies to a specific type of golem though.
Wizards also get an arcane discovery to speed up crafting by 25%. It doesn't specifically mention constructs, but it says to select one type of magical item, and I'm sure you could argue that constructs are one giant item.
So Wizards are the best.

Gwynbleidd |
although for thematic and RP reasons you could also argue Alchemists and Witches are also good candidates for constructs since both offer very nice flavours slants on crafting constructs. Alchemical Golems etc.
The Alchemist was personally the only other class that struck me as a real possibility but I haven't really looked at the Witch at all.
Although it should be mentioned that in most adventuring timeframes crafting a golem isn't really possible unless your GM is willing to grant you some time concessions.
My GM is usually willing to give us downtime, heck we had about a month (in game) of downtime.

Interzone |

Wizards are for sure the best, but they are also the obvious choice which will often turn me in another direction in itself :P
There are at least a couple AP's that allow for a lot of downtime at certain points, the one I'm doing right now had a whole year off, although it was fairly low level at that point so there wasn't a HECK of a lot that could be done in that time, but nonetheless... was awesome for my character with Craft Wondrous Item :D