The Dragoons prefer bold color schemes that emphasize their presence on the battlefield. Unit aerospace fighters are commonly painted bright “canary” yellow or fiery orange, though the classic red-on-black scheme is still prevalent. BattleMechs are typically painted solid colors; red, gold or black are favored hues.
Beta Regiment paints all its machines emerald green.
Per FM: Merc (revised), page 112-120.

Other references:
Warhammer, CM: Mercenaries (p 110)

The Dragoons’ insignia is a black, snarling wolf’s head set on a circular red field trimmed in black. Beta’s insignia is the Greek letter B painted on the left legs of ‘Mechs, left wings of fighters and left fenders of all vehicles.
Per FM:Mercenaries Revised, pages 113-120.