This is intriguing. Definitely the kiwi as one, but surely the ostrich as the other?
The elephant bird (Aepyornis maximus), an extinct flightless bird of Madagascar, also known as the "giant bird" or "roc," laid the largest known bird eggs. Some of these eggs measured up to 13.5 inches (34 centimeters) in length and 9.5 inches (24 centimeters) in diameter. The largest egg produced by any living bird is that of the North African ostrich (Struthio camelus). The average size of this bird's egg is 6 to 8 inches (15 to 20.5 centimeters) in length and 4 to 6 inches (5 to 15 centimeters) in diameter.
The smallest mature egg, measuring less than 0.39 inches (1 centimeter) in length, is that of the vervain hummingbird (Mellisuga minima) of Jamaica.
Generally speaking, the larger the bird, the larger the egg. However, when comparing the size of the egg with the size of the bird, this does not always hold true. The ostrich egg, for example, is one of the smallest eggs relative to the bird's body size. And the hummingbird egg is one of the largest eggs relative to the bird's body size. The Kiwi bird of New Zealand lays the largest egg relative to body size of any living bird. Its egg weighs up to 1 pound (0.5 kilograms).
Sources: Cruickshank, Allan D. 1001 Questions Answered About Birds, p. 174; Walters, Michael. Birds' Eggs, pp. 12-13; Wood, Gerald L. The Guinness Book of Animal Facts and Feats, pp. 90-91.
Relative Size
Although large birds lay larger eggs than do small birds, small birds actually have proportionately larger eggs. It takes 60 ostrich eggs to equal the weight of one ostrich but only nine hummingbird eggs to equal the weight of the Calliope Hummingbird. The birds that lays the largest eggs, relative to body size, are the kiwis of New Zealand. Kiwis are about the size of a chicken but lay eggs that are about 140 mm long and 90 mm wide, about three times the size of a chicken egg. It takes only four kiwi eggs to equal the weight of a kiwi. Fortunately, female kiwis lay only one and occasionally two eggs per year!
The ostrich egg is the smallest egg in relation to body size laid by any bird