Preheat the oven to 350°F. Grease a standard-sized loaf pan or 3 mini loaf pans, then cut a piece of parchment paper to line the bottom, leaving enough overhang on each side that you can grab easily to remove the baked loaf.
In a large bowl, rub the lemon zest into the sugar for about 1 minute. Whisk in the yogurt and eggs until well combined, then whisk in the flour, baking powder, and salt. The batter will be thick. Now whisk in the oil and keeping whisking and stirring until smooth. Fold in the cranberries.
Pour the batter into the prepared pan or pans, then place in the oven and bake for 45 minutes for 1 loaf, or about 30 minutes for mini loaves, until a tester inserted in the center of a loaf comes out clean. Place on a wire rack to cool in the pan for 10 minutes, then use the parchment paper to gently lift out the loaf and let cool cool completely on the rack.