I've just used pure turpentine to get a dried (dark) emulsion paint stain off a white roller blind and it seems to have worked. It's a relief - thought I'd have to get new blinds... (The emulsion was Colortrend 100% acryllic if that's any help).
If your paint is latex (water-wash-up) then rubbing alcohol should disolve it. If it is oil-base, then mineral spirits may work. I'd try a small less noticable area to test out first...Either could react with whatever your blinds are made of. (If you use mineral spirits, you need to wash it off afterward as it is flammable.)
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