The Mercedes book "Faszination SL 230SL - 280 SL (W113)" on page 27 (english translation) states the 230 SL had a production run of 19,831 units from March 1963 to January 1967. It was also worth noting that the export share of 230 SL production was 59 percent. The US export share was only 24 percent. Considerably less than for the predecessor 190 SL (40 percent).
I expect there are other sources that can confirm this info....
The production stats in the technical manual are as follows:
Numbers are the last vin number for each month listed.
63 January none
February 000002
March 000003
April none
May 000018
June 000037
July 000142
Norm