binscatter uses a colormap to show densities. Setting binscatter to a single color would defeate the purpose of the function because density would no longer be visually represented. I suppose a use case of applying one color would be to show the range of 2D coordinates contained in the data. Note that binscatter does not currenltly have alpha mapping which could be used with a single color to indicate density (similar to geoscatter).
Nevertheless, set the colormap to a single color if you only want to use one color.
x = randn(1,100)*20;
y = randn(1,100)*15;
% Default appearance
binscatter(x,y)
% Apply single color
binscatter(x,y)
colormap([.07 .44 .75])
