Hines, 26, has made five appearances for Boro this season, while Nouble, 23, has played twice for Ipswich this term.
"In Seb we have someone who brings great experience and adds quality to the squad," Sky Blues manager Steven Pressley told the club website.
"Frank's ambition certainly aligns with my expectations."
Meanwhile, midfielder Carl Baker has left Coventry by mutual consent after four years and 28 goals in 182 appearances for the club.
League One side Coventry City have signed Middlesbrough defender Seb Hines and Ipswich striker Frank Nouble, both on loan until 4 January.