Applying DeMorgan's Theorem to NAND gates leads to the idea that the gates closest to the output work as OR gates and the next layer back work as AND gates. Signals that enter at odd layers are inverted. So, no, you probably can't get there with 4 NAND gates. Try to implement A*B + C*D with (3) 2-input NAND gates and you'll see what I mean.
OTOH, the output of NOR gates closest to the output work as AND gates and the gates one level back work as OR gates. Signals that enter at odd layers are again inverted. Try to implement (A+B) * (C+D) with (3) 2-input NOR gates.
For your project, the following should work:
Output 1 = NOR( A, NOR( B, B)) -> B AND (NOT A)
Output 2 = NOR( B, NOR( A, A)) -> A AND (NOT B)
Look at the first equation. Notice that A is entering at the output NOR gate, an odd level. Hence it is inverted. The first level NOR is still working as an AND gate and NOT B is the other input. So, that NOT B is inverted at the output to become B and the final equation is B AND NOT A.