Posted: 28/03/2017 at 14:45
Problen, the preparation and sowing of another small lawn will be expensive as would decking. To start you would need to remove the stones, dig down and remove what ever is underneath saving some of the stones for drainage. That will mean around twelve inches deep. You would then lay some of the stone back as drainage but then need to replace around ten inches of soil of reasonable quality, Loam or Compost mixed with your own soil and plenty of washed sand. On that pan after raking all small lumps and bumps from the pan, any stones or clumps of clay depending on what you used in the mix walk up and down it shuffling along (the gardeners shuffle), this will firm the top for laying the seed or rolls of grass from a Garden Centre, with children a medium grass would be needed.
OK that is how you would lay a lawn and the better you want the lawn the deeper you would dig and the more topsoil and sand mix you would lay under the grass. I am assuming time will also be a problem so I cannot believe I am saying this and will wash my mouth out later. Remove stones, lay a membrane and then Astro Turf, it is like a carpet for children to play on if you get the correct one, the early stuff could cause burns if you slid on it. I await the screams of traitor from the gardening world but often needs must.
New builders get away with murder, laying six inches of soil onto the compressed pan of the building site then roll out cheap rolls on that. We get the cries of help on this board and it hurts to tell them the truth which is why I explained lawn laying. Time and Finances being an issue you have to cut your coat, as an old time gardener my way is do it properly, do it once, short cuts mean you do the same job over and over.
Looking at the picture again, dig the stones out check the soil underneath if it is reasonable dig it over, remove lumps and stones then lay turf rolls. It would last until you have more time and money.