You might find an overall wiring diagram for the generator, but the AVR will be listed as a empty/black box. You can get the P/N for that board assembly, but I would doubt you will ever find a discrete component list for the AVR. This isn't really rocket science, but it can be made complicated depending on if any other control functions are piggybacked onto the AVR circuit.
On another forum I participate for slow speed engines, a few are working on a simple AVR circuit to enhance the simple harmonically excited generators a lot of us are using on our slowspeed engines. These generators don't use an AVR. It has a diode rectifyer pack and some brushes. It uses load dependent feedback from an extra set of stator windings to excite the field. Because of this it has a looser voltage tollerance. Mine goes from 125V down to 115V between no-load and full load, and this is mostly attributed to the RPM/freq droop from 62HZ down to 58HZ full load.
This freeware AVR they are working on will cost about $30 or so in parts to fabricate. The current plans can be downloaded and someone is working on getting circuit boards etched at a minimal cost, to aid in our home construction.
There are a bunch of different ways to excite and control a generator, that all the manufacturers circuits, and that particular burnt part, are going to be different. A good electroincs engineer with a way to make an educated guess at the other components on the board might be able to tell you what that damaged part is.
There are also a few generic AVR manufacturers out there, but knowing enough about the application to order one that would work, is the hard part...