All five wheels to include the spare received the same paint process per John Z's tech article The First-Generation Camaro Assembly Process.
From my observation, the DG wheels made in calendar year 1967 are dated coded, but it's inside the rim where the tire cannot be mounted to see it, and the format is month and YY. I've never seen an early model year 67 DG wheel with a 66 year code, and I've seen some with no date code which I assume are early cars. I'll see if I can post a picture later.
A DA wheel would not be used as a spare for a car with J52/DG wheels. All five would be DG code. The DA wheel cannot clear the front calipers. As the CRG Chassis/Wheels section indicates, only cars with a full wheel cover would have black painted wheels.
As already mentioned, a later service replacement would have the date code by the valve stem hole, same as 68 and up.