Sometimes, black eyes are due to many factors that can thin your blood or make you bleed more during surgery and afterwards. Genetics, medications, technique of the surgery, etc can all play a part.
When you ooze more during and after your procedure, you will tend to develop more bruising. Two months is rather a long time to resolve this, and it may be due to your circulation and general health. Also, with a facelift, the lymphatics that drain your eyes and the pathways from eyes to your general lymph system and circulation are sometimes impeded due to the area of the facelift. Your eyes drain towards the angle of your jaw, below your ear. This is the exact area that is manipulated during the facelift and can impede the drainage of your black eyes.
Exercise and sometimes massage and warmth can help. Black eyes can also be due to iron deposits from blood where your bruises where located. This is harder to treat but can be the same treatment as with persistent bruising, i.e. exercise etc. Sometimes, people also attribute prominent veins to the appearance of black eyes. If these are veins or blood vessels, time will improve them. Sometimes lasers can help decrease the appearance of these vessels. The only way you can find out is by having someone look closely at it.