My first bet would be to find a seller and ask for some images of the cards. They'll usually accommodate a potential customer.
After that, consider that you need not necessarily follow the original color patterns to the letter. Think of your market: are you selling to people who can read Arabic and understands the suits? If not, coloring the suits in different colors might be a good idea. If you're trying to make a deck that's useable in games normally played with an International-style deck, you could pick shades of two colors and use a shade for each suit. For example, deep blue, light blue, deep red and reddish-pink.
I scoured the German site, but no Mamluk cards. The Japanese site, on the other hand...
The cards look VERY elaborate. Was it hand-painted?