Ha. Just went though this, and the threads I found on here were confusing.
You need to enable the second joystick by checking the checkbox in the joystick controller panel. Set the joystick to Set 1, and only set the shortcuts you want to use for the left joystick (joy1). Be certain you only use j1up, j1down, j1left, j1right in this dialog. Delete any key references to j2. Now set the joystick to Set 2 using the dropdown, and assume this is for the right stick (joy2). Instinct will have you wanting to set shortcuts for this stick using j2up, j2down, etc.. but THIS IS WRONG! You instead, STILL WANT TO USE j1up, j1down, j1left, and j1right. Again, remove any references to j2 anything in the shortcut dialog.
I don't *think* you need to set anything in the cocktail dialog, but to be safe, I set the bottom joystick definition to be Set1.
I finally got mine working, but figuring this out took some time and much irritants. I believe MaLa assumes j1 is a dpad on a gamepad and j2 is the analog control on the SAME gamepad (think ps2 controller). I'm not sure how one would word this to make it clearer, but it's fairly confusing at face value.
Let me know if this doesn't do it for you. I'll assume you've got your mame.ini set up to use joysticks and your issue is MaLa only.
-csa