As already mentioned, an after-market barrel and a 9MM mag should do it.
However, I notice Brownells sells both P229 40/.357 recoil springs and P229 9MM recoils springs – so apparently there is a difference. You might also need to get a 9MM spring, esp. if you plan on shooting milder 9MM ammo in your P229.
Note that the P229 .40 mag is fatter near the bottom than the P229 9MM mag (which is the same as the P228 9MM mag). The 9MM mag will definately work in your pistol, but the fit will be a little sloppy.
Note also that the .40 P229 has a slightly wider breachface than the 9MM P229, though apparently this isn’t a major issue.
Thus, while I think a converted P229 would be a nice plinking/training pistol, IMHO it really shouldn’t be trusted as a self –defense handgun.
When ordering a 9MM barrel, make sure it’s for a .40 P229, not a 9MM P229. It’s easy to mistakenly order the wrong one since both are available.
IIRC, a few weeks ago a couple of members posted sources for conversion barrels in a different thread (either here or maybe in General Handgun Discussions). If you go back a few pages you might be able to find it.