I'm sorry I can't provide you with a more favorable answer. It is difficult to comment more specifically without having a copy of the HOA rules and regulations and being more familiar with how they have been enforced in the past.
Assuming the rules do not provide relief, and I would again urge you to review them carefully, the apparent conflict of interest and/or abuse of power by the HOA president can be brought up at the next meeting.
Unfortunately, with HOAs, they have a system in place to deal with these matters and courts tend to loathe wading into these types of disputes before the complaining homeowner exhausts those procedures.
How long will the drywall be stored? Depending on the amount of money involved, is this a situation where it might be cheaper to beg for forgiveness then to seek permission? The rules should give you an idea of the type of fine you could face.
Assuming the rules are unfavorable (and again, we need to confirm this) - Have your brought up to the property manager the apparent inconsistency with how the HOA/ management treated the president's situation versus yours?
Did the HOA president seek permission from the HOA before the dumpsters were placed in front of his home? This might have been the case and, if so, it may set a precedent for getting similar permission.
I would consider bringing up these inconsistencies in writing to the property manager (and definitely cc the President and HOA board) and ask the manager for permission to store the drywall. If you put the matter in a broader context (that the president was given more favorable treatment) and the HOA board knows you are aware of this, perhaps they will relent and you can get permission without having to resort to a meeting. Bit I would get any approval given in writing.
When the property manager denied your request, did they cite any specific HOA rules? If not, I would request they provide you with the specific rule they are using to deny you permission. This might help you save time when looking through the rules.