Go to this website: http://boatschedule.leytonms.com/index.php
Check the settings for the ferry leaving FROM Basseterre TO Charlestown, click on Friday or enter your planned date of travel, click on Show Schedule. Use the scroll bar on the right side of the page and scroll to the bottom of the listings, there you'll find the evening ferry departure times.
The ferry schedules can vary slightly depending on day, date and/or time of year so it's aways wise to check, however, generally speaking on Friday the passenger ferry leaves from Basseterre at 6PM and 9PM. The SeaBridge Car Ferry (also takes passengers) leaves from Majors Bay on the southern peninsula at 7PM.
Your other alternative is to take a private water taxi to take you from St. kitts to Nevis. The staff at your resort or the management company for your rental villa can arrange this for you but it is not cheap.