this is mostly trial and error approach. i've selected suspension vertices and disabled/hidden other vertices, so they don't get affected incidentally. by default, entire suspension part (right side) was fully influenced by suspension_rf bone (bright right influence color on a model loaded with no "slice to parts"). I've set "chassis" bone as "current bone", switched ".mesh" to vertices level and painted chassis influence with:
pressure: 10%, hardness: 0%. it is done in several touches: paint from hub to chassis mount part (low influence, blue color), then paint again from spring @ hub to chassis mount again, then from second coil spring turn to mount, then from third spring turn to mount... and you get a gradient of influence on spring from blue (low) at hub to red (high influence) at chassis mount. The image shows influence of chassis bone (looks like a bit of bug, it should be blue to red, but it's blue->cyan->magenta (some color channel is messed, but it's actually ok):
and the same part with suspension_rf bone influence: (made some refine touches too, to make gradient more accurate):
meanwhile, during painting, you can switch to object mode and rotate suspension bone to see in 3D the real effect. you can even leave suspension bone rotated (and 3D view showing stretching of spring) and still be able to edit/paint in front/top viewport and seen an effect instantly. I used to switch to object+rotate bone and switch back to verts to paint.. Yup it takes some time to get used to it, but then it's not of much effort afterward.