What kind of filter do you have on this 10 gallon? With a good filter you could probably do 15 neons, they have very little bioload. If the filtration is not so good, 10 should be fine. Neons aren't the most hardy fish though, and won't survive a cycle. You should either do a traditional cycle with danios and trade them out for neons later, or consider fishless cycling, there are lots of threads here that explain how it works.
One more thing, the neons i have access to at most of the stores are inbred and weak and there seems to always be at least one carrier of neon tetra disease in any batch. If you can afford to use cardinals instead, you could have a couple less total fish (say, 8 with mediocre filtration. 13 with good filtration) but they would be hardier. I know that books all say cardinals are weaker but in my experience the books are out of date. I recently did a fishless cycle and stocked all the cardinals in my sig, and didn't lose a single one. When i buy neons, i usually get around a 50% initial mortality rate within the first 48 hours. Maybe i am just unlucky?