Everyone's body size, drift pattern, approach etc is different, so no, there isn't any one specific system that works for everyone. That being said, what I find the easiest to remember is to try to think of spares as being groups. For example the 3, 6, 10 would be a group and I use 3rd arrow to hit the 6 pin. Where I stand is a matter of trial and error, but once I know where I'm standing to hit 3rd arrow and the 6 pin, that's it. From now on that's where I stand for the 6 pin because, in theory, my plastic ball should go straight everywhere I go.
Now that I have a starting point for the 6 pin, I can experiment moving my feet left for the 10 pin and right for the 3 pin. Once you know those spots, you can split the difference between them for combos like the 3,6 and 6,10.
You could do the same for the 5 pin, then move from that to convert the 8 & 9 or the 2 & 3.
Honestly, using a plastic ball makes shooting spares absolutely simple as long as you know and remember where to stand and where to throw. At that point, the only thing causing you to miss is your accuracy.