Mind your own business is a ground cover plant, low and delicate. It's great for covering ground, brickwork, anything really. However it likes plenty of water and some shade, it won't take full sun.
It can be spread by dividing up clumps. Works best with on a compost bed. I should think you could get it to cover the stone it you work at it slowly, from the base upwards. Dividing established clumps and tacking it on a bit at a time. Keep well watered and never let dry out completely though even if you do it may come back over time to recover. I once created a very successful terrace garden by clearing clumps from a friends garden where it was a nuisance, which it can easily become. It's great in the right place and there's several types, a silvery green and a golden green, along with the green green! Try not to walk on it or let animals pee over it. Also clear away dead leaves and other shading, rotting material from lying on it.