According to the Laws of the Game substitutions are allowed during any stoppage with the permission of the referee. Note, many competitions and leagues with unlimited substitutions disallow substitutions on corner kicks.
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According to Law 3 of IFAB's Laws of the Game, a team may substitute players at any stoppage of play, including corner kicks.
Many youth leagues allow for an unlimited number of substitutions. In order to preserve game flow and prevent this from being used unfairly by a team ahead in goals to waste time, such leagues will limit subbing opportunities. In these leagues, subs are not allowed when play is to be restarted with a corner kick, free kick, penalty kick, dropped ball, or the opposing team's throw-in. The throw-in restriction is usually waived if the team taking the throw is also subbing.
If your league allows more than three substitutions per team, check the rules for subbing restrictions.