Well there is my 1986 (verififiable date of first registration) with a 427 side oiler, for instance. Any ERA less than number 175 or so would qualify, mine is ERA154, the 154th car built by ERA. It left the factory in 1984, but wasn't first registered until 1986 (in Texas) by the SECOND owner. The original owner never completed the car. Anyway, 2nd owner sold it to Calif dude who sold it to me. It's complete history is well documented (thick book) in the EAAC registry (Ernie's American Automobile Company).
Others that would fit the requirement would include: Hi Tech (no not the MODERN HiTech, the OLD ones), Contemporary, Arntz Butler (but very few if ANY came with a side oiler). What is interesting about the older replicas is your much more likely to find a really accurate build. A number of Hi Techs and Contemps are incredibly well done in a 'period correct' type manner. To duplicate such a car today would easily run over a $100K. 20 years ago or longer replica makers/builders were much more inclined to really get in there and 'do it RIGHT', 427 was a 'must have', for instance. There were fewer cars, they were more exclusive, they cost a BUNCH!
Then manufacturers like FFR started a new trend in replica design, aimed at the 'masses', low cost, using donor parts (Mustang, small blocks, etc.). This opened the door to a much larger car buying audience and in general was the beginning of the 'it's only a replica, what the hell' kind of build philosophy. SPF continued the trend by not offering 'kits', more consistent quality and in general a drop in the 'period correct' outlook. SPF is very common with 351W, 429, 460 for instance. A few with side oilers, but not generally the rule. BDR then entered the market with it's low cost offering and pretty well sealed the fate of 'old school' replicas. Now days pretty much anything goes to the point where the only thing that represents an original Cobra is the general body shape (and some even mess THAT up with wings and air dams). Whats next? Freakin' curb feelers and neon lights? A front wheel drive Honda powered Cobra can't be that far off!
Now I TOTALLY understand the foriegn market (England, Australia for instance) where laws and other restrictions leave a guy little choice but to consider alternate engine power, side pipes optional, etc. etc. Hey, you gotta do what you gotta do, better to have a replica 'sort of' than none at all (I guess).
But wait, here we have an Aussie actually LOOKING for an FE side oiler??? Whoa, give that man a beer! Well done mate! Makes me just want to shed a tear, hope lives on 'down under'.