Yes, you can! In fact, some people find labret-style piercing jewelry more comfortable to wear than the typical nostril screw because the flat backing sits flush against the inside of the nose.
There a few things to consider when purchasing labret or tragus studs to use as nose rings:
Inserting labret posts into your nose piercing can be kind of tricky because you will have to put the jewelry in through the inside of your nostril - it helps to have an appropriately sized pin taper to use (these are made specifically for inserting internally threaded or threadless jewelry). Start by inserting the taper through the outside of your nostril, line up your jewelry with end of taper, and then carefully pull the taper and jewelry back through the piercing.
You don't have to use a pin taper, however, it will make things easier because the end of the jewelry won't slip off the end of the taper as you start to pull.