I don't have a California coupe, but there's quite a lot written on the German forum, and on there the 113-750-03-77 seal is confirmed as the correct part number. 113-790-00-83 is the seal for standard W113's
MB never referred to the option as a California Coupe, so it's not surprising that dealers or the Classic Centre get confused
Authentic Classics and Niemoller list both seals, Authentic Classics state theirs are genuine MB parts, and the prices for both are similar
When i looked at our registry list and searched California Coupe, there were probably less than 10 listed, i think out of about 800 registrations, but this could be misleading due to the descriptions used. When i looked at the German forum, it looks like there are no definitive numbers of these cars produced, best estimates seem to be as little as 2% ordered with this option, but this could be pure speculation