As in your provided dates, days are same, so you can create 12 new rules for the months and set different color for each month.

After selecting the whole range of dates (Assuming your dates are in col. A and starts from cell A2), create a new rule with the following formula.

=MONTH($A2)=1
While using above formula in conditional formatting, you can fill a color of your choice and do it for every month by changing the red colored number 1 to 2,3,4...12 and change the fill color for every month. This is the only way as far as I know.