Lab puppies are a completely different species than adult Lab dogs :- ) They are furry, needle-toothed vampires, and they will not stop nipping unless you beat them with a large wooden cross or shoot them with silver bullets... However, be careful about beating them, b/c they may take it from you and chase you with it !!!
The Bite Stops Here takes about 3 days to begin to make a difference, but there are some subtleties that may help. After you say Yelp, Ouch, Oops, ... or even "You SOB!!!" The pup may apologize in the form of a bark or a slight playbow. If you don't accept the apology, you get bitten, ... if you accept the apology you also get bitten

but the dog will begin to understand his infraction.
With a Lab you will have to withdraw attention repeatedly to get it through his near indestructible skull that other creatures (such as you) can be hurt by a nip... This explanation may help:
Read this and note the 3 days and the apology....
Some Tweaks to Bite Inhibition (to get him to stop biting when he wants to play):
1. When the pup bites, then yelp. It should sound about like what the pup does when you step on its paw... don't step on his paw for a sample

. When you yelp, the pup should startle briefly and stop nipping. Praise and pet. He'll bite.
2. When he bites the second time, Yelp. When he stops, praise and pet. He'll nip again, although it may be a little gentler. ...
3. When he bites a third time, Yelp (see a pattern?). But this time, turn your back for 15 - 30 secs. If he comes around and play bows or barks, then that is an apology. This is important. Accept it, praise and pet... and cringe in expectation of the next nip...
4. When he bites the 4th time, Yelp, then leave the area, placing him in a 2 min. time-out. It is better if you can leave, rather than moving him. Then, return and interact. (He's still hungry...)
5. When he nips the fifth time, yelp, and leave the area, stopping interaction for now.
Pups need to sleep over night in order to learn their lessons. So, keep doing this for 3 days. By the third day, you should notice signficant Bite Inhibition. He may still nip, but it will be softer and he won't draw blood. Keep up the training and make sure that everyone yelps.... Very powerful method.
If you learn the technique, then you can apply the "yelp" to other circumstances, also. I believe that "yelp" is "Please don't do that, I don't like it." in dog communication. I currently use the yelp when my dog plays tug, then runs with the toy, when he fetches and keeps it out of reach or when he takes a treat too quickly....
Progress is slow, but please try it over the weekend and let us know your progress...