Tribal Power Armour can be repaired by NPC's such as Moira Brown or using 'standard power armour' such as Brotherhood of Steel power armour or Outcast Power Armour. You cannot use Tesla Power Armour, T-51b or its winterised variant, Enclave Power Armour or the Medic Power Armour.
Tribal Power Armour is difficult to keep in good condition. My advice is to kill any Brotherhood Outcasts in a random encounter. Loot as many suits as you can and store them in your house/suite. Also, if you have the Operation Anchorage DLC and have finished it, you may loot the Outcast Outpost for all power armour, gaining about 5-6 full suits.