If it's run through DosBox, you could map keyboard keys to your joystick buttons.
In DosBox, press control+F1 to open the keymapper utility. In there, you can map the arrow keys to your gamepad's d-pad for instance, and the control (jump) and alt (shoot) buttons to whatever gamepad button you want.
First, click the keyboard button you want to map. Then click the 'Add' button at the bottom, and then press the button on the gamepad that you want to use for that action. Do that for all the game buttons, and then press 'Save'.
I'm not entirely sure if it caries over between game launches, and if it's a game-specific setting or if the mapping is for all Dosbox-run games, but it should work this way.
If Dosbox does forget the settings between launches, you'll have to set the 'mapperfile' setting in the Dosbox config file to the stored map file.
I hope I'm making sense >_>