In a word: DON'T
This topic has come up in a few forums I participate in. As usual, I've put a link to an excellent article at the end of this entry but wanted to add a few thoughts of my own.
The Alpha Roll was popularized by The Monks of New Skete in their book "The Art of Raising a Puppy." In the second edition they retracted and apologized for the advice. Dogs just don't do it, and people do not have the capability to read the signals if it were appropriate.
In the 30+ years Dr. David Mech has been studying wolves, he said in an interview that only three times has he seen what he would consider an Alpha Roll (if I remember correctly, but certainly less than five). But this also goes back to what I've said before, that dogs are not wolves.
So, what are we seeing? Remember that dominance is not a personality trait, but an aspect of a relationship. Just because one dog is being aggressive or acting inappropriately, it does not mean he is dominant. He does not become dominant until the other dog submits. However, that relationship may change in seconds.
Take for example if I'm walking down the street and someone walks up to me and punches me in the face. Who's dominant? If I fall on the ground crying then I have made the other person dominant in that situation by submitting. But what if I hit them back? Does that make me dominant? It all depends on what the other person does. And so it goes.
Back to the question, what are we seeing? One thing may be play behavior. Play in dogs is usually mock hunting or mock sexual behavior. In mock hunting, the dogs will chase, nip, soft-bite, etc. One dog may roll over on his back, exposing his belly, but the dog does this willingly. This can also be a way for one to say to the other "I'm am not a threat. We are just playing."
In another instance, we need to remember that dogs are much more scent oriented than we are. When greeting, we've all seen dogs sniff each other's back sides and genitals. One dog my roll over to expose their genitals and make them more accessible.
And another instance would be access to a resource, whether it's a toy, food, or whatever one or both dogs may want. In the face of a potential conflict, one dog may submit to the other saying "you want that much more than I do, so you go ahead." As shown the Bristol study ("Dominance in domestic dogs – useful construct or bad habit?," October 2009) that may change depending on the next resource, situation and desire for that resource.
The take away message is that dogs are not dominant by nature, they do not Alpha Roll, and even if they did, we could not tell when it would be appropriate, and all it does is scare your dog and damage your relationship.
http://companionanimalsolutions.com/blogs/dangers-of-alpha-rolling/