Nothing in the rules prevents a creature with Multiattack from taking a bonus action. This is all the DM's Basic Rules and Monster Manual have to say about Multiattack:
A creature that can make multiple attacks on its turn has the Multiattack ability. A creature can’t use Multiattack when making an opportunity attack, which must be a single melee attack.
Although it wouldn't matter in this case, the bonus action bite could occur before the deinonychus finishes its Multiattack. See the Player's Basic Rules or Player's Handbook, under Combat, The Order of Combat, Bonus Actions:
You choose when to take a bonus action during your turn, unless the bonus action’s timing is specified, and anything that deprives you of your ability to take actions also prevents you from taking a bonus action.
The only requirement for the bonus action is that it occur after knocking the target prone, so it can occur during the Multiattack. This doesn't prevent the Multiattack from finishing.
Additionally, Jeremy Crawford (the lead rules designer for 5th edition's rules) has confirmed that the bonus action from Pounce occurs on the same turn, just in case there was any doubt.