The peacocks of Grace, Arizona are an inheritance from the founders of the town, the Gracela sisters who came over from Spain to marry a bunch of miners, with their peacocks in tow. The peacocks are a symbol of Grace's history—remember that the Stitch and B**** club decides to sell their peacock piñatas with a history of Grace rolled up in their beaks.
The peacocks are also a symbol for the matriarchal history of Grace: these birds are the opposite of the fighting cocks. That's why the piñatas are the symbol for the women's fight to save the town. The men, it's made clear, are content to try and use a lawsuit against the mine, not caring that it will take way too long to get any results. They're also the ones with the dynamiting skills, and while the women seem more than willing to use violence against Black Mountain, those skills stay with the men, who won't use them for fear of being arrested.
Instead, the women use peacocks. The only kind of awkward thing here is that all their peacock piñatas represent male birds—peacocks, not peahens. Never fear—Kingsolver takes care of any possible misinterpretations of the symbolism here by having all of the male peacocks molt their impressive tails right after the Stitch and B**** river summit:
On the way back Viola was quiet. She walked quickly, stopping only to pick up the feathers that littered the leafy orchard floor. The sudden cold snap that heralded the certainty of winter had caused the male peacocks to molt in unison. There being no hope of mating for months to come, they had shed their burdensome tails. (16.52).
Basically, the males have directly passed their most powerful and impressive feature, their tails, on to the women to use.