Weeds Constantly Appear Between The Stone Slabs On My Patio. How Do I Get Rid Of Them?

Basically, unless you want to raise up the stone slabs and fit a membrane underneath them to prevent weeds from re-curring (which would be a huge job), you have two options.  Either you can remove them by hand or you can spray them with weedkiller.
Some weedkillers can creep sideways through the soil, so they cannot be used near to the edge of a lawn or flower bed.
However, a number of weedkillers which are less toxic can be purchased from garden centres or DIY stores and these can be used near to the edge of the patio, but they are less potent and do not remain active for very long.  
Some people find that actually burning the weeds off involves less labour than hand weeding and reduces the amount of toxic fumes.  Specialist weed burners are now readily available and whilst not a permanent solution, may be useful in your case.