I can't think of the employment of a tense, which conveys your intended meaning. The closest I can get to one is:
"He would have done anything you asked him to."
Though this may not be totally immune to misconstrual, as it may suggest contingency on a condition.
"He would have done anything (if condition were true) you asked him
It's true as others have suggested that it's simpler to say:
"He would do anything you asked him to."
But this isn't totally unambiguous, as evidenced by the meaning apparent in:
"I would do anything you asked me to."
This doesn't necessarily refer to the past. "Would" doesn't have to refer to the past, eg.: "I would go but I don't have the money".
And "asked" doesn't necessarily refer to the past either, as evidenced by its meaning in:
"If you asked me to jump off a bridge, I'd tell you to go to hell."
It's possible that the most clear way of conveying your desired meaning is to do what FumbleFingers said in their comment, that is, qualify the sentence with extra information as to a time you're referring to:
"Back then, he would do anything you asked him."
- Courtesy of
By specifically including "back then", you make an implication that the statement you make applied earlier, but no longer does. But this is an implication, not a necessity.