well you could buy one..
Generally, a hook on a pivot is used, such as some sort of block with a small hole through it,in which the hook uses as its fulcrum, so when you pull the line(whatever you are using to launch the balls) tight, and then hit the end of the hook so it levers(?)upward and releases the line...
Also, a hole-pin is used, A small loop or equivelent(thing) is attached to the end of the line, And a hole is made in a predetermined position(eg.between the two guide boards of a ballista), So when the line is pulled tight, A pin is inserted thorugh the holes and line,and when ready to fire the pin is removed(quickly)....
the latter could be considered safer since you dont have to be as close to the ballista when you want to fire it(attaching long string to pin) dont know if this would be a problem for you though....
this might be helpfull,
http://www.instructables.com/id/SLT34AXFRXUSX66/
you should post a video when your done....