As someone who has painted many odd surfaces (even ones that refuse to take paint such as silicone caulk), it is all in the primer. I hate to even say this, but here is what I would do if forced to:
Remove the grill and tweeters/woofers, plus pull out the connection box in the back that holds the speaker wire clips. Basically, remove everything that you don't want paint on that can be removed. Carefully put painter's tape over the decal sticker in the back. This will all help to make it look like it was SUPPOSED to be painted.
Then, using a medium grade sandpaper maybe around 180-220 grit (remember the smaller the numbers, the more viscious it will attack the surface). Just a light, but even "scuffing" of the surface is what you want. Do not "rub" the surface, but lightly and slowly "swipe" the surface going "with the grain" so that it retains the wood texture look after painted. Take your time...
If you have some canned air or a compressor, blow the dust off of the surface and out of the woodgrain "pores". Then, using a damp (not wet) cloth, or better yet what is called a tack cloth, remove any and all dust from the surface. I've had some luck using even a cleaning product like "409" or "Windex" and spraying a cloth and then wiping the surface to help really make sure it is free of any grease or oils from your hands.
Now that the surface is prepped, decide how you are going to paint it. It would be ideal if you could paint a thin coat on ALL surfaces and then have it dry, but that would mean either hanging it or propping it up through one of the holes where the speakers were. Test out your mechanism before trying to hang or balance a painted speaker.
If you are going to spray, make sure that you plug any opening that is there because the speakers are missing. If rolling on paint, then you could probably cover the holes with painter's tape.
I have found that a spray primer is easy to use even if you aren't using a spray paint in the end. Make sure that the primer is designed to work with vinyl, and DON'T get the cheap stuff. You are going to be painting a $600 pair of speakers, spend $10 and not $2 on the primer. Remember that a couple of light coats is WAY better than a thick one. Test the spray on a piece of cardboard to get a good feel for how far away you need to be in order to be effective. Most primers want a 2nd or 3rd coat to be applied BEFORE the previous coat dries. Keep this in mind. Also, your 1st coat shouldn't completely cover the surface. If it does, then it is probably too thick and could end up with waves (like really wide "drips") on the surface. I would say that the 2nd coat would be really close to 100% coverage, and a 3rd coat should do it perfectly. Again, if you go too heavy, it will take fewer coats. Now, some super premium primers can do it in one coat, but they are usually applied with a comercial grade sprayer. I've also used primers that are in a spray can that claim "1 coat," but I still get better results doing a couple lighter coats.
So now it is drying after being primed.
Painting is a similar process. A couple light coats vs. one heavy one. Since you are trying to blend them into the wall, I am guessing a laytex interior paint. Just paint the speaker as you wish. A good quality paint can be brushed on and the brush marks will disappear. If you are in doubt, I like little foam rollers for something like this. Cloth rollers tend to leave a texture. Foam rollers are smoother. Take your time as this will be the finish layer to the speaker.
So at this point, you are letting the paint dry. After it is dry to the touch, but not fully cured, move any of the painters tape if possible, being careful around the edges that it doesn't pull up your finish. Let it completely cure (24 hours?) before putting the tweeters, woofers, speaker wire connection back on.
As for the grill, I have no idea. Any additional paint will reduce sound transmission through the grills as it basically decreases the "holes" that the sound can go through.
