You should have a number of different sets of numbers on various parts that could be used to determine the engine's year. Each block and head should have a 4 digit date code cast into it. On the engine it is on the front (distributor side)and will be something like L078 or M026. Decoding is simple. The first character is the month and loosely follows the number placing in the alphabet. (A=January, etc.) There are some variations to this in specific years, but generally it follows that pattern. The next two digits are day, and the last is the year. (ie. 6 could be 1976, 86, or 96)
You'll also have an 8 digit number something like 10101496. For the Fiero 4 cylinder "R" block there are generally 1 or 2 different numbers per year, and you could have either of them. Sorry, I don't have the actual list of numbers for the 84 Fiero. I did, but I lost them. You should be able to get the yearly casting numbers for Pontiac R blocks from any engine rebuilder. I am also working on an 84 Fiero SE with my son, and I found a Frankenstein engine in his car that you could encounter. Apparently during a 1988 recall, GM replaced a number of engines with an "engine kit". This kit contained a long block and exhaust manifold and had the casting date M028 for the block and L078 for the head(at least for mine). It had block casting number 10044562 and head casting 10101496. My engine rebuilder tells me that the head casting is a common number used from 85 to 88 on select R engines, but the block number is a special run of blocks from 1988 that were built to the 1986 spec. What you are also likely to encounter if you should find one of these is a crank with the gear to drive the balance unit installed in 88, connecting rods marked 987 (used only in 87 and 88), roller cam and lifters, and pushrods that match the 88 length spec.
According to the Haynes manual, there should also be a stamped number on the front of the engine near the water pump on a machined surface. This number should be decodable to give you year, model, and other info. Unfortunately, my frankenstein was missing this stamped number because it was supplied as a replacement kit.
Please remember that this is based on my research and experience with my engine. GM may have a variation on the above tale.
Hope this helps.