If you choose for the creature to gain haste, it gains haste indefinitely. It won’t lose it as the turn ends or as another player gains control of it.

If a creature entering the battlefield has riot but can’t have a +1/+1 counter put onto it, it gains haste.

Riot is a replacement effect. Players can’t respond to your choice of +1/+1 counter or haste, and they can’t take actions while the creature is on the battlefield without one or the other.