Not sure if this is optimal, but I'll conjecture that the best arrangement is to optimally pack coins at each depth layer (and coins do not cross horizontal layers).
The number of layers of coins is 90cm/1.88mm.
The number of coins per layer is around (area of box bottom)/(area of coin) * (packing density) = (40cm)^2 / (pi*(25mm/2)^2) * (density) where density is about pi/(2sqrt(3)).
See Sphere packing - Wikipedia, the free encyclopedia to understand why this is the packing density.
Final answer is about (number of layers) * (number of coins per layer) = 477 * 295 = 140715 coins.