Prior to the British takeover in 1797, Tobago was Spanish and using Spanish gold (the doubloon of 16 pesos) and the peso fuerte, divided in 9 bits. The money of account was the peso sincillo of 10 reales. The official rate of a peso of 8 reales was not observed. Since the price of the doubloon overvalued gold over silver, silver would have been driven out at a rate of 8 bits, so the dollar was devalued to 9 bits.
Even this didn't stop silver exports, due to an unpaid trade surplus with Britain. Pridmore mentions a cut dollar of 11 bits in 1798, made 12 bits in 1811 (KM 12) as well as the piece cut out, a moco of 1-1/2 bit (KM 9). Both pieces are rare and there are many more forgeries than originals. He also lists a number of counterstamp TB on copper Cayenne black dogs with (KM 6) or without (KM 5) annulet. These are very hard to come by. Moreover, all antedate the 1630's by a wide margin.
I think that if any money circulated on Tortoga around 1630 it would have been Spanish colonial silver in the name of Philip IV. These are not hard to find and not overly expensive. Moreover, they are badly struck and have just the right "look" for the book.
Attached is (my determination) a peso 1627-1629 Potosí (now in Bolivia).On the left is a cross with lions (Léon) and towers (Castilia) in a floral design. On the right is the Habsburg coat of arms with P•T (my interpretation) on the left and the denomination on the right.