According to Santa Cruz chemicals it should be soluble in alkaline water. Adjust the pH first and try solubilize it in stages(i.e. add a known small amount every time)
As to how much Para Red you will have to find out by trial and error. I would guess 1mg/ml is to much. I suggest you try dissolving 1 mg in 1o ml alkaline water - make sure your solution is totally clear (no turbidity) and has noticeable color. If 1mg/10ml does not give clear solution add water sequentially and measure final volume when clear.