William 4th was only King of England for Seven Years so the number of Gold coins minted were fewer.
He introduced a smaller Half-Sovereign in 1834 but this was not popular with the Public or in commerce.
Although Silver Crowns were not struck during the reign of Willam the Fourth, proof or pattern crown silver coins were made but are quite rare.
In Gold Coins the following were minted :
Two Pounds (only as a proof)
Gold Sovereign each year from 1831 to 1833
Small Half Sovereign in 1834 only
Larger Half Sovereign
In 1835
1836 (rarer)
1837 (Scarce)
British Valuable Coins :
Articles include :
http://greatgoldcoins.net/about/
http://greatgoldcoins.net/british-gold-coins/
http://greatgoldcoins.net/british-gold-coins/british-hammered-gold-coins/
http://greatgoldcoins.net/british-gold-coins/british-sovereigns/
http://greatgoldcoins.net/valuable-gold-coins/
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1834 William IV Half Sovereign PCGS AU 53 US $1,200.00
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1835 WILLIAM IV GOLD ALLOY PATTERN CROWN US $15.47
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MASSIVE The Ultimate Sportscard Collection XMAS US $9,499.99
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1816 Silver Half Crown George the 3rd XF US $40.00
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KING WILLIAM IV PATTERN CROWN GOLD COIN ENGLAND 1837 US $6.19
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CHRISTIES FRANKLIN ROOSEVELT COLLECTION RARE US $69.99
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All of the Gold coins of this reign are much more valuable in EF condition.
Coins of this King usually make Good Investments

US $1,200.00