Layers > New Fill Layer > Solid Colour, default will be black - just click ok.

In the layers pallet, set the blend mode of this fill layer to Colour Burn, then double click the black square icon beside the name to open the configuration window again.

Pick your colour, somewhere in oranges/yellows will normally suit a Sun Print replication. The colour I used is #D58925.

Looking at the result so far, the colour is fine but levels and brightness/contrast could do with a little change.

Layers > New Adjustment Layer > Brightness & Contrast

Fiddle around until you are happy, I'm using +35 Brightness, +6 Contrast

Similarly with Layers > New Adjustment Layer > Levels, tweak the settings until you get the levels of shadow, midtone and highlight you want.