This will not be a simple matter.
Without MCAS (or a system that effectively does that function), the aircraft cannot pass part 25 of FAA regulations (transport aircraft) because the nose can pitch up more than the commanded (yoke) input without it.
A. Use both AoA sensors and both electronics units and if a disagree occurred (not an uncommon issue apparently for the AoA sensors on the 737) then MCAS gets out of the way and a cockpit alert is issued.
This would require a massive amount of total simulator time (once they actually get the simulator to properly recreate the actual aircraft handling) apart from other training. It will also incur quite a significant cost for the electronics and software involved (although that is a one time cost).
I am not sure the regulators outside the USA would permit a duplex system that disengages at a critical phase of flight (by definition, it only engages when it 'thinks' the aircraft is about to enter a dangerous phase of the flight envelope), but it would be a potential method.
B. Add a third AoA sensor (and pitot tubes apart from a great deal else) and a properly designed triplex computing system for a properly redundant triplex system.
This would require a complete rethink and re-statement of the system requirements and might be achievable in a couple of years (not including flight testing) but re-casting the system to level A (which it should have been anyway) will incur a great deal of testing and review (at the hardware, software, mechanical and system level).
Either option would require pilot training and re-certification which would not be a 'standard' 737 certification which means the airlines would not be able to schedule any '737' pilot to any aircraft. That would put the airlines off (they were the ones, after all, who were demanding 'just another 737, but more fuel efficient', without pilot re-training costs and simulator time).
Either option makes this a 'new' aircraft, in my view (others may differ).
I cannot see how this problem could be addressed without doing one of these (apart, of course, from just scrapping the programme in it's entirety which includes, lest we forget, the 737-8, 737-9 and 737-10).
I also cannot see it while the bean counters are in charge although they should be crying about all the beans they did not get to count this time.
The FAA might approve the design, but a complete re-certification from the other regulators around the world is likely to take years anyway.