As far as one ounce bullion coins are concerned, several countries make them. Canadian maple leaves, Australian kookaburras, Chinese pandas, British britannias, Austrian philharmonics, Mexican onzas; all are popular. There are also plenty of modern commemorative "coins" out there.
If you're after formerly circulating coins, there are plenty more to choose from. In world coin collecting terminology, a large "dollar-sized" coin is called a "crown"; this is named after the large silver 5 shilling coins called "crowns" once issued by Britain and several British colonies. British crowns are slightly larger and heavier tan a US silver dollar. A "crown" in either the general or literal sense can be either silver or cupronickel.
Australia, for example, only made one type of "crown", in 1937 and 1938. Sterling silver (.925 fine), mintage a bit over a million, weight 28.27 grams. The design looked like this (picture snitched from djluster's CCF gallery):

There's even a reference book for people who are only interested in crowns and dollar-sized coins: "World Crowns and Talers" by Davenport. It lists large silver coins going right back to the joachimsthalers of mediaeval Bohemia, the distant ancestor of the "dollar".
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