There's bound to be more than one way, but I'd start by going to 'settings' from the splash screen then to 'controller assignments'. From here make sure you have activated the joystick (it's selected as the controller in the joystick window). CFS2 (or Windows in general) will auto-assign functions to the number of buttons you have (or at least it did with my 12 button thing).

To find out what assignments have been given to the buttons you can either scroll through the list and look for 'joystick button 1, joystick button 2 etc', or you can try to reassign a function. Pick something from the list at random and tell the game you want to assign a new key to that function. A new dialogue page comes up asking you to indicate what you will use. Hit the fire button (usually given as button 1) and see what happens. If CFS2 has already assigned it to something you'll get a warning. Cancel the change then press button 2 and so on. This will give you a list of the auto assigned functions for the joystick. This will tell you what you need to re-allocate later when you get the buttons to drop bombs and stuff.

The entry you are looking for on the list for bombs and rockets is 'release selected ordinance'. It has no default joystick assignment. It is done with the enter key.

Piers

PS, the default key to cycle/select ordinance is the backspace key.