The statement that God can raise up stones as children of Abraham could mean that
As God built Israel upon the rock of Abraham (Isaiah 51:1), so he can create children of Abraham from stones, stressing that salvation is for the spiritual, rather than the physical, descendants of Abraham (see Romans 9:7–8; Galatians 4:21–31), including, possibly, the heathen nations. OR
The image of stones stresses that only God can make us his children. God can raise up children of Abraham through divine regeneration (see Jesus’ connection to John’s preaching in John 3:3, John 3:5).
Interpretation 1:
Just as God built Israel from the rock that is Abraham (Isaiah 51:1), so he is also able to raise up children of Abraham from stones. This also highlights the fact that salvation is for the spiritual descendants of Abraham as opposed to the physical descendants (see Romans 9:7–8, Galatians 4:21–31). The stones therefore possibly serve as an image of the heathen nations.1
Interpretation 2:
The image of stones is used to preclude every thought of human merit, shifting all focus to the work of divine regeneration. If you are not born of the God of Abraham, your natural descent from this patriarch does not benefit you at all. God can even raise up children of faith for Abraham without such a natural descent through regeneration (see John 3:3, John 3:5, where Jesus draws a connection to the preaching of John)2
9 et ne prétendez pas dire en vous-mêmes: Nous avons Abraham pour père! Car je vous déclare que de ces pierres-ci Dieu peut susciter des enfants à Abraham.