Put this in a new Stylish style, modifying the colors as you wish:
#appmenu-button{
background: -moz-linear-gradient(top, rgba(58,127,197,1), rgba(47,119,189,1), rgba(0,58,229,1)) !important;
}
#appmenu-button:hover{
background: -moz-linear-gradient(top, rgba(78,147,229,1), rgba(0,78,213,1)) !important;
}
#appmenu-button:-moz-window-inactive{
background: rgba(0,0,0,0) !important;
}
It worked for me when I tested it just now. The current colors give you a blue Firefox app menu. If you want to have the main color stay around (instead of "disappearing") when the Firefox window is inactive, remove the #appmenu-button:-moz-window-inactive{...} section.
(Note: I used the link in the answer provided by CGA to figure out how to do the first two sections, and added the third section based on my own search.)