Comment I've done it. (Score 2) 324
I had one critical advantage. Our HOA board members were being complete dicks about the clause in question(*) - so much so that the management company (a third party paid by the HOA to run things in accordance with state law) was sympathetic to me, a new home owner, and advised me on the exact process for changing the covenant.
With their advice, my wife and I created a one-page proxy form which we took door-to-door and got our neighbors to sign, one at a time. It took a month, but we eventually got proxies from just over 75% of the owners.
(*) I have since learned that this is pretty much the natural state of all HOA board members.