Basically you will struggle to find a more gentle and loving dog than a greyhound.
However he is a DOG and this point must never be forgotten. It is rare to hear of a greyhound who has bitten a human but in most of these rare cases it has resulted from the same cause.When he is sound asleep he is a dog and if he is suddenly disturbed in his sleep his first reaction could be to defend from attack. In the wild, nature would force him to do this and before he has fully awakened this reaction will have kicked in.This means he may accidentally bite his beloved owner before he realises what he has done. To the uninitiated this is a dog attacking a human, which it is certainly not. Solution? Do not waken the dog violently, (children can do this accidentally) let him waken up and your friendly boy will be back in the land of the living. The moral is "let sleeping dogs lie".