I've searched high and low for information on production dates and engine serial numbers for the 2H - with little success.
. There are two types, early and late. The early type was made from 1980~85, and has sleeved cylinders. The later type is a parent-bore block (no sleeves) and was made from 1985~90. These two types are pretty tough to tell apart on the surface. One difference is in the oil cooler cover, which had an early narrower mounting for the oil filter bracket, and the later type which is wider.
Which vehicle is this engine out of, an HJ47 or HJ60?
The block serial number is a bit longer than the one shown in post #2 above, and I don't notice a yy/mm/dd sort of pattern to it myself. The longer Toyota part number mentioned above, which is cast on the block below the oil cooler cover (left side of the engine) does give a clue as to whether the engine is the later type or the earlier type - please post up the number of yours and I'll compare it to mine and that will help narrow it down. If you don't mind posting up the block serial number, I can tell you if your engine is earlier or later than the 1986 engine I have.