American goldfinches do not visit feeders as often in the summer as they do at other times of year. One way to get goldfinches to visit your yard is to grow plants they like. Generally, the goldfinch is a seedeater, preferring seeds from birch and alder trees, burdock, chickweed, and dandelion. But they also eat the leaves of Swiss chard and beets.
If you plant a vegetable garden, you might want to add a row of beets or red chard just for the goldfinches. They will feed on it all summer. While goldfinches do eat the leaves of white Swiss chard, they seem to prefer red-stalked varieties. Because they take small bits of leaves, you will see little holes throughout the entire leaf.
Why goldfinches eat chard and other greens is not known, but perhaps it is because Swiss chard is high in calcium. Other members of the finch family are known to nibble on mineral matter containing calcium, including gravel along roads where calcium chloride has been spread to melt ice.