How to stop meatballs falling apart when frying
You might consider a different approach - don't fry them.  Drop them (carefully) into a pot of boiling sauce instead.  They come out perfectly even, very tender, and more flavourful than frying.  Usually the sauce we're talking about is a sweet tomato-based sauce, but it could be anything that's reasonably thick (so that the meatballs don't just fall straight to the bottom).

This sounds counterintuitive to a lot of people - you might think it would be more likely to fall apart this way, but in practice it sets almost immediately because it's suspended and has a much more even heat distribution.  When frying, all of the heat comes from the bottom; it's the combination of pressure and weight (gravity) that makes it fall apart.

Perhaps you want the rougher, browned texture of pan-fried meatballs, and that's fine; but I thought I would mention this anyway because I can distinctly remember dozens of guests having come to the family home (this is a family recipe, after all) asking "how are you able to make the meatballs like that?"  So if you have a chance, just give it a try; you might be pleasantly surprised.