First, the contenders:
1.) Red Cedar, Juniperus Virginiana. Eastern/aromatic red cedar. From "The Directory of the Historic Cabinet Woods" by F. Lewis Hinckley.
"The red cedar, Juniperus virginiana, also known as the pencil cedar, is indigenous to the eastern half of this country and to the West Indies; attaining a height of about ninety feet and a butt diameter of more than three feet. .........
Supplies of red cedar were received in England during the seventeenth century. The wood imported from Virginia was noted by Evelyn as "nearest to the Bermuda juniper, both yet exceeded by that from North Carolina." "
2.) Spanish Cedar. From the above resource: "The Spanish Cedar, Cedrela odorata, is native to tropical America and in particular to the West Indies, producing an important hardwood timber that is alternatively known as Havana cedar, West Indian cedar, bastard Barbados cedar, swamp cedar and cedrelas. This tree is not a cedar in the botanical sense, as it belongs to the mahogany family (Meliaceae), but the wood does possess a fragrant scent which is quite similar to that of the true cedars.... Supplies of Spanish cedar are available in dimensions up to forty feet in length and forty inches in width......
Prior to the middle of the eighteenth century "Spanish Cedar" was also received in the American colonies, and stocked by our leading cabinet shops. However, where "Cedar" or "Red Ceddar" are mentioned in old inventories of raw materials or home furnishings, or "Red-Sedar" - appearing as early as 1711, it is problematical whether these names apply to Spanish cedar or to the native red cedar, Juniperus virginiana, for both of these woods have been referred to as red cedars in the past."
3.) A possible third contender is "Bermuda Cedar". Again, from Hinckley:
"Bermuda cedar, Juniperus bermudiana, provided the colonists of this small island group with a principal material for the construction of their furniture. Accounts of the earliest visits to Bermuda mention a great abundance of cedar trees resing above the other endemic growths....The oldest specimens are recorded as attaining trunk diameters of about three feet, a measurement contrasting to the very small size of timbers later observed by Laslett.........
Bermudian craftsmen employed the island cedar in constructing chairs, tables.....chest, cabinets,...
Prohibition against the exportation of Bermudian timbers [in 1632]........was cirumvented to some extent by embodying cedar planks in packing cases......These planks were frequently used in width up to thirty inches or more......"