Assuming it was in the same system as Rigel X, it was presumably located less then ninety lightyears from Earth. This is because Enterprise visited Rigel X before it visited Risa, which in "Two Days and Two Nights" was said to be ninety light years away and the furthest Humans had ever traveled from their home.
According to Star Trek: Star Charts (pp. 52, 59, "United Federation of Planets I"), Rigel II, also known as Beta Rigel II, was an M-class planet. The planet was a member planet of both the United Rigel Colonies and the United Federation of Planets. Rigel IV was admitted, along with the United Rigel Colonies, to the Federation in 2202.