What color do you suggest?

gray

Paint it a darker Maroon or Burgandy color

I suggest a brighter popping color towards a burgundy or even an 'orange' - what's found within the stones

Emphasize the welcoming aspect of a front door. I suggest a light yellow door along with the same yellow for the pillars - your entrance will recede with a dark color. When winter and dark days come, a fresh, light color will not seem out of place. Can you add a light fixture and house numbers (not black) in the apex of the roof? White shutters are classic and crisp. The black planters make the entrance narrow - place them along the left edge as a safety feature because of the drop off between the cement and the yard. Paint them yellow, orange, whatever and fill with matching flowers. Yard sales have pots, too. Use a larger outdoor mat, L.L.Bean's "Waterhog" are quality, lasting mats, in colors. - if this entrance is used in winter you may want a boot scraper also.

I would pull a color that you like out of the stone

Try Turquoise for the Shutters or maybe Caramel or Spring green or Pale Olive. The door I like as is, but may be make more of it by standing a tall plant next to it or a Hanging Basket etc.

Slate blue with white trim or a deep egg plant with white trim.

I love the idea of black with your pretty house. Here is example of the great contrast it provides with paint and and stacked stone....https://www.houzz.com/photo/3640407-north-laguna-2-contemporary-exterior-orange-county

The painted shutters against the paint and stacked stone sections bring a continuity and marry the two different materials together...https://www.houzz.com/photo/92432-2008-parade-of-homes-house-mediterranean-exterior-denver

This entry POPS! https://www.houzz.com/photo/10286457-stacked-stone-exterior-transitional-exterior-orlando

This is accessorized perfectly....https://www.houzz.com/photo/6691279-kensington-period-apartment-traditional-entry-london