These cards were distributed by the Long John Silver restaurant chain back in 1990 over an 8 week period. Each week, the restaurant would hand out a different cello pack that contained 6 cards: a header card plus 5 player cards.
There is a great picture of the entire set, complete with all the header cards on Fuji's blog [relink], but I'm just interested in the two cards that I recently acquired. (Incidentally, that blog post by Fuji is from 2011 - thank goodness the Internet never forgets!)
Card Number 769: Starline Long John Silver, 1990; #4
These would have been given out in the packet distributed in week one of the two month promotional period.