The roof deck glued and screwed to the top chord of the joists will provide the lateral stiffness you need if you're using 2x4s.
Since the store-bought 2x4 is actually 1-1/2x3-1/2, and the 1x2 is actually 3/4" thick, you'll end up with a member 4-1/4" tall. You might try a load test with an ordinary 2x4 and a 2x4 with a 1x2 glued and screwed flat to its bottom chord. Significant improvements in bending stress may also be made by adding a flange to the bottom chord of your joist. Still more effective, if you are only concerned with the height of the joist at the top of the wall and can stand some camber in the top deck is to take say a 2x8 and radius the top chord into a fair curve, so that you have a 2x8 at the center, which is the point of maximum bending stress. Click to expand.Without getting into calculations, one way you could get greater stiffness with a 4" thick member is to increase its width, say going from a 2x4 on edge to a 3x4 or a 4x4.
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