The only practical solution currently is rubber bullets. The cops get to keep the ease of use and most of the stopping power of a gun but the lethality levels go way down.
"Stopping power" is a myth -- a rather obvious one if you think about the physics. The bullet can't carry any more energy than is imparted on the shooter, and actually carries less.
People who are shot stop for one of four reasons.
1. People stop because they know they're supposed to fall down when they get shot. That is, the bullet doesn't actually do any incapacitating damage, but they fall down anyway. Rubber bullets might be able to do this, but it doesn't work on everyone, and once everyone knows the police are carrying rubber bullets, it will work on even fewer people.
2. People stop because the bullet did structural damage that prevents them from being able to move. Mostly this means broken bones in strategic places. For example, if a bullet shatters an ankle or a knee, you're going to have a hard time walking. If a bullet shatters your pelvis, you will be completely unable to even stand. Rubber bullets can't do this reliably, and might not be able to do it at all.
3. People stop because the bullet severely traumatized their central nervous system. Shoot someone in the head and they'll (usually) switch off like a light. Rubber bullets might be able to do this, sometimes (e.g. penetrating through an eye socket, or through a thinned area of the skull), but not non-lethally. Very high-powered rounds can also achieve the same instant lights-out effect through hydrostatic shock. A large-caliber rifle round to the upper chest, for example, might not do lethal damage (assuming treatment is quickly available), but might generate a hydrostatic shock wave that slams into brain and/or brain stem with enough force to temporarily disable the target. Handguns cannot do this, it requires enough energy that it's really only feasible to get from a weapon with considerable recoil, enough that you almost certainly need a stock to transmit the recoil to the shooter's torso. Rubber bullets carrying that much energy would probably penetrate, assuming it was even feasible for police to regularly carry high-powered hunting rifles (note that mid-energy weapons like AR-15s can't do it).
4. People stop because they black out from blood loss. This is the primary goal of shooting someone with a handgun, to create a hole (or, more likely, holes) that open up large blood vessels, causing the target's blood pressure to drop dramatically, reducing blood flow to the brain and causing a blackout. It's most reliably achieved by several bullets into center mass, into the large mass of organs and blood vessels in the torso. Rubber bullets can't do this. And if they could they'd be no less lethal than lead bullets.
So, no, rubber bullets do not provide "stopping power". They're useful for harassing people who are willing to run away when faced with painful bruises, and they have the advantage (to the police) that the bruises can be delivered from a distance. But against someone you really want to stop? No way.