Where can I find a parts list and diagram/schematic of a Bryant #588ANW048080ABAG combination AC/gas heat unit?
I need the burner covers that independently cover the back ends of the burner unit. Their purpose is to prevent gas from being blown away by the wind or escaping the burner area and allowing the unit to run normal when gas is called by the sender wire. Without them, the unit will only run a few minutes and then shut off because it cannot detect gas all the time.

Have you contacted the Bryant company and asked them what sort of replacement covers they recommend for your unit? Usually aftermarket burner covers can fit several models and Bryant would know what models fit your older unit.