Some people have conditions that cause hand tremors and such, so I try not to assume anything, even though personally I have no trouble handholding my own 24-70 without IS.
I'd suggest 24-105 IS, 28-135 IS... they offer pretty close to the same image quality (it would be hard to tell apart 11x14 prints from each), even if they lack the f2.8 aperture of your 24-70.
If you still need f2.8, you might look at third party lenses... Sigma has some fast ones with OS, their version of stabilization which is pretty comparable to Canon's IS. There are also some VC Tamrons and VR Tokinas, but I really don't know very much about them.
I'm afraid a 70-200 will simply be too long for a lot of portrait work on a crop camera.
Prime lenses really don't help, though they might have larger aperture that allows a slightly higher shutter speed.... Canon 50/1.4, 85/1.8 are very good portrait lenses. 100/2 is another possibility, though starting to get a little long on crop cameras for some portraits. There is also the Tamron SP 60/2.0 macro/portrait. But, there's no IS on any of these.
Shorter lenses that might work include the EF-S 17-55/2.8 IS. The EF-S 15-85mm IS actually has a wider range of focal length than your 24-70, but is f3.5-5.6.
Yes, a tripod would be ideal... a monopod is a possible alternative. And, without knowing your level of experience, simple practice and working on hand holding techniques can make for a lot of improvement.