I has been trying but I dont have the case, Those are the first time I am learing to script.
You can do this using a script in ServerScriptService, along with the following: PlayerAdded PlayerAdded will return Player
You can then use Player to find when their character is spawned using CharacterAdded. This will return the player's character.
then use:
for i,v in pairs(character:GetChildren()) do if v:IsA("Part") then end
This will go through every item inside of a player's model and see if it is a part. v stands for what item is being checked. If v passes the test and IS a part, then you can use BrickColor.random() to give the part a random color.
v.BrickColor = BrickColor.random()