Citizenship by descent
For people born before September 19, 1983: Any person living in St. Kitts, who was at that time a British Dependent Territory Citizen (BDTC) or a British Citizen was eligible for St. Kittsian citizenship as well as their child born or adopted abroad and their foreign national spouse.
For people born on or after September 19, 1983: A child born abroad, at least one of whose parents was a citizen of St. Kitts and Nevis.
Registering a child as a citizen is done through National Security, and the process usually takes around three months from the time the citizenship application is submitted (more details here).
US - Adult $250, Minor $100
UK - First time application fees - £125 Minor - £75 Minor. Additional £75 Fedex fee plus possible additional charges according to the High Commission in the UK.
British passport holders don’t need a visa to holiday in St Kitts and Nevis. On entry, you will be granted a specified period to stay. If you wish to stay longer you must apply and pay for an extension of stay through the St Kitts and Nevis Immigration Department.
For US citizens, a tourist visa is not required for stays under 90 days.