Closest two frequencies that can be resolved
There is no issue of frequency resolution in a typical modulation and demodulation scheme. (unless you want to implement some frequency/signal detectors)

Putting two message signals in adjacent channels requires that their spectrums do not overlap. In your case you should be able to specify the associated bandwidths of those two slowly changing analogue signals. 

Assuming that associated (baseband) bandwidths of those signals are $F_1$ and $F_2$ Hz, then the carrier frequencies $f_{c1}$ and $f_{c2}$ have the relation: 
$$ f_{c2} - f_{c1} &gt; F_1 + F_2 $$ 

That's the minimum distance allowed for classical AM modulation, you could have used, instead, a single side band AM (SSB-AM) which would reduce the minimum distance to :
$$ f_{c2} - f_{c1} &gt; \min(F_1,F_2)$$

But definitely that would require a more complex and difficult modulator and demodulator in terms of implementation.

Assuming that you have met this criterion (and assuming that you have selected the simple classical AM option), after down-converting, demodulating you should sample the signals satifying their respective nyquist rates.