Gnocchi is already a very hearty dish; deep frying it sounds positively deadly!
You need a good pan to make crispy, pan-fried gnocchi. Ideal is a heavy cast iron skillet, well seasoned. Alton Brown has an excellent description of how to season a cast iron skillet in his book: "Gear for your kitchen". It's basically a coat of vegetable oil to the pan, placed upside down in a 350 degree oven for an hour, then turn off the oven and let the pan set until it's cool. If the pan has a wooden handle, you may want to remove it before putting it in the oven. Otherwise the handle will acquire a nice seasoned look too:)
Once you have your seasoned skillet, it will function like non-stick cookware! Heat the pan (you can leave it on medium-high or even high heat pretty much as long as you want until you are ready to cook, then add a SMALL amount of good olive oil. The French expression is a "filet d'huile" or a "thread of oil". If the pan is hot, the olive oil will get hot very quickly (but not as fast as butter, which burns REALLY FAST. Butter is good too, though. Just adjust the pan temp down a little first). Throw in the gnocchi, add a little thyme, rosemary, etc., and shake the pan back and forth over the burner like Jiffy Pop until the gnocchis are golden brown on all sides. If you want to get fancy you can lift one edge of the pan like an Italian chef and make the gnocchis hop into the air a little bit to make them turn.
Crumble a few pinches of "fleur de sel" (flake salt) over the top between your thumb and forefinger, and you will soon be eating a heavenly dish.
Note: don't cook this dish too often unless you are really skinny and are trying to gain a few pounds!