.You could probably solve this through trial and error, but you can get a good basis for the solution decently quickly with logic. For each queen to not attack each other, you'll have to put them in their own row, both horizontally and vertically. We also know that the queens will be sharing four black and four white spaces between them, because any queens sharing the same colour can be attacked, if arranged improperly. To that end, here are two solutions I found:
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Golden_Scroll found a third solution, described following the standard chessboard pattern of A1 being the bottom left corner and H8 being the top right: "A6, B4, C7, D1, E8, F2, G5, H3."