A simpler version of the methods suggested in the FAQ, which is a sticky on the forum. Maximum skill is 100.0 for Carpentry.
From 50 skill (assuming the character has access to the Samurai Empire craftable items):
At 50, Start with Ballot Boxes, which use a lot less wood than anything else. If you want, you can switch to wooden shields at 52.6, but that's only if you want to sell the items to make back some of the gold you invested in buying wood.
At 60.0, Make Fukiya (a type of Blowgun)
At 70.0, Make Bokuto
At 80 or so (as low as 78.9, or as late as 85), Make the Gnarled Staff or Shepherd's Crook all the way to 100
Gnarled Staves have been the traditional method, but if you can become a friend of the Britain Library, it is better to do the Shepherd's crooks, and donate them for collection points. The only hard part of that quest is getting a friend to go kill the speckled scorpions to give to a non-combat crafter (or doing it on another character, and getting them to the carpenter before they time out).
In fact, if you do the library quest before you hit 70 skill, you can donate both the Bokuto (the Samurai at the library) and the Shepherd's Crook (the animal trainer, upstairs at the library). Donation might take a little longer, but there are substantial rewards for doing so (the minstrel & alchemy talismans can help a crafter add more skill points to their template for making some of the music or magery items, to put in other crafting skills). If you make fishing poles (require some tailoring, and can be started slightly before the bokutos become available), those can be donated to the fisher, as well.
Alternatively, you could find someone that regularly donates to the Library, and arrange for them to be around when you are training, and you sell them the items so that they can donate them, at a fraction of what their point value will be (a library donation point can be bought for 15 gold a point, so selling the items for 5-10 gold per point of their donation value will get you back more money to buy more wood). If you don't have Mondain's Legacy on the account, selling the items to someone that does will be your best bet.
This assumes, of course, you are using an account that has been upgraded since age of shadows. If you're using a REALLY old new account code, that doesn't have access to Samurai Empire or Mondain's Legacy, you would switch from ballot boxes to wooden shields at 60, add 40 tailor and start doing fishing poles at about 69 skill (they become available a few skill gains earlier), then switch to gnarled staff or Shepherd's crook at 79 skill. The ideas of finding someone to buy the fishing poles and crooks for donation still holds true, even if you can't donate them yourself.