The Jaegers do not use any specific paint scheme, but instead paint their machines appropriately to the mission.
Per FM: Merc (revised), page 59
Thunderbolt, FM: Mercenaries Revised (plate 8)
The Jaegers’ logo shows a boxer dog (fawn coloration, black muzzle, ears cut and standing straight up) standing in profile facing left, on a Steiner blue circular background whose edges fade into the camo pattern of the unit. The words “51st DPJ” appear above the boxer. ‘Mechs and battle armor display the logo on each shoulder, while vehicles display it on the glacis of each turret and aerospace fighters on both sides of the fuselage. Any additional numbering identification appears below each insignia. Per FM:Mercenaries Revised, page 59.