Don't stain it black. If you want a black door, sell that one as it's a very nice door, and buy a cheap metal door you can paint black. I would have that one refinished if it was my house.

Personally I always build outdoor pergolas and decks with Trex or some other brand of engineered eco-friendly lumber alternative. The initial added expense is completely recouped in the lack of maintenance and need to keep re-staining and repainting. But since yours is already built, I would say tat using a really good primer (like Kiln's) is key to having the finish last longer and having it look better.HEre is a guideline: Primers fill the pores in wood and form a good adhesion base for topcoats. They’re lightly pigmented to help the topcoats cover better. Oil-based (alkyd) primers are the old favorite, but high-quality acrylic latex primers are now available and a popular choice of many pros. Both work well. In either case, be sure to buy a quality product and spread it to the proper thickness. Better primers are more expensive. Read the directions on the label to determine the ideal application thickness. A common mistake is applying it too thinly, like a wash, rather than as a regular coat. When priming cedar or redwood, use an alkyd primer or a stain-blocking acrylic latex primer. Cedar and redwood have water-soluble tannins in their heartwood that, when moist, will leach out and “bleed” through the topcoats, leaving dark, ugly stains. Alkyds and stainblocking acrylics bind the tannins and hold them in the primer. Buy a brand from a dealer who will guarantee the product’s performance. Knots can also bleed through the topcoats. To prevent this problem, double-prime them. First prime just the knots with the alkyd or stain-blocking acrylic primer or pigmented shellac (such as BIN). Let the primer dry, and then prime the entire wood surface. TIP: Choose your paint first, then read the label and buy the primer recommended by the manufacturer. Some paints perform best when used with the same brand of primer.

Give some thought to stain it a gray close to the color it would naturally turn to. This will give it the protection of the stain with much of the look of a weathered color. Another bonus is that this is the color that it wants to turn to so it will look better for a longer time than any other color. I would use a semi- transparent stain for a more natural look even though it will not last as long as an opaque stain.

Thank you for posting the photos, normally I can tell right away what my opinion is but I can't come up with one this time. I don't want to steer you wrong. Maybe I need a photo of the entire house and this is probably the reason I can't decide. I'm one of those people when I'm buying myself cloths or jewelry, I need to see myself in a full length mirror, even when buying earing's so I can see myself as a whole. With a house I need to see how painting the poles black would affect the rest of the house. It is a bold statement and would need to work with the house as a whole, not just the porch.