You will need to make sure that what you have created is in fact a true parody. In general, it should be commenting on the artist, the work or the message of that work directly.
If so, then we would consider that "fair use." But fair use is a defense, what really matters is whether the copyright owner of the work looks at it that way. If not, they can take action and force you to mount your fair use defense. Depending on the court in which the matter is heard, the outcome may vary.
You may want to have a lawyer offer an opinion before you stick your neck out so-to-speak. Most of us here, including myself, offer a free phone consult.
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If the painting is no longer protected by copyright then you can lawfully create your own work based on the painting [which may be why there are so many other derivative works]. If not, then you very likely need permission from the painting's copyright owner. You need to speak with your own copyright attorney to check the copyright status of the painting.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
The key is whether or not the painting is still covered by copyright.
Discuss all the specifics with an attorney in your area.
If your painting is a true parody, it may qualify as fair use. But many people do not understand the distinction between parody and satire. A parody is a work that is directed to commentary and criticism of the original work and its author. A satire, on the other hand, is intended to constitute political or social commentary which is not necessarily linked to the original work or author. If, as I suspect, your painting is a satire, then the fair use doctrine will be less likely to apply.
Moreover, there are times when a famous painting can become a trademark--and your use of a trademark in this manner could create market confusion or dilute the value of the trademark. Your use could also be considered a form of unfair competition to the extent you are attempting to gain commercial profit by associating yourself with someone else's famous work of art.
In a situation like this, the devil is in the details and you should retain and consult with intellectual property before proceeding with this project. Only by having a precise understanding of what painting you want to use, how you want to use it, and what your image would look like, could I begin to provide meaningful advice. There are no shortcuts here and you should not use Avvo as a substitute for retaining legal counsel. Your proposal carries severe economic risks for you, and if you want to proceed you need to invest in legal counsel.