You'll need to wipe down with white spirit to remove as much residual surface oil as you can and leave a couple of weeks to give it chance to dry out to the extent that a paint coating has a chance of adhering.
I'd suggest an aluminium wood primer as a first coat which will aid adhesion and also block the staining. Then you have a choice of a conventional oil-based matt finish such as Coo-Var Matt Black
Or, Zinsser AllCoat Matt Black which is a water-based self-priming finish. You take a risk with this product in terms of adhesion and long-term performance though. There is also a chance that you still get some staining coming through.
Also, bear in mind, matt black paint is not, by its nature, reflective and will absorb high amounts of heat and ultra-violet radiation which will break down any paint coating over time and denature the wood material beneath. You should, therefore, ensure that the paint coating is maintained at regular intervals to counter this.