Just a few stamps with readable circular date stamps. The large size of the stamps has allowed for that information to be captured. I have 120 stamps of this issue but only 20 actually have the strike I am seeking. In working with the stamps I have, I have seen a range of year dates from 1903-1937. I suspect some collectors who were around at the time the issue was current made an effort to get such postmarks for their collections.
Maybe they mailed their stamps to the postmaster for the post marking service or they visited the island as a navy seaman, a merchant mariner or a tourist. I am glad they did so as it allowed some nice postmarks to be "discovered" all these years later. I know that some postmarks were arranged by a collector because often all the stamps in the series have the same date.
St. John's is the most common postmark naturally being the capital.
I did find a couple St. Mary's and partials of other smaller postmarks, but I have been unable to ascertain their names. I was surprised at first to find some Barbuda postmarks, but like it says on the coats of arms in Latin, Antiguae et Barbudae.

ST. JOHN'S 21OC03

ST. JOHN'S 04NO03

ST. JOHN'S C 09NO15 with a control letter "C" in the postmark

ST. JOHN'S 29JU04

ST. JOHN'S 04MY04

ST. JOHN'S 28AP04

BARBUDA 05JA24 thank goodness for favor postmarks -otherwise this postmark would be very elusive

ST. MARY'S 28SP09 the best I could find for St. Mary's on this issue

ST JOHN'S C 07OC09 another postmark with a control letter "C"