Under FIBA rules (ie real basketball rules
) The head coach is the ONLY person that may request a timeout. And strictly speaking, the request must come before a deadball opportunity.
In other words, once the ball is dead, a timeout cannot be granted for that dead ball period. Obviously this is not rigoursly enforced, and if the situation permits it, the official will usually grant a timeout, even if the ball is already dead.
Unfortunately, with the spread of the NBA-style rules, and the increase in the number of players watching NBA games on TV in Australia, many, many players and coaches believe that a player on the floor may request a timeout. This is worsened by the fact that our professional league (the NBL) also allows timeout requests from players, including whilst the ball is live.