There was no Irish 1840 Halfpenny minted.
The Irish currency was withdrawn in 1826 and the British currency was used in its place.
Due to Britains ongoing expenses with various wars in the late 18th and early 19th centuries, there were very few silver or copper coins minted, subsequently there were a great many privately minted tokens and counterfeit coins produced.
To get an estimate of value on a privately minted token, you need to provide the details of the inscription on the token.
The value of a 1959 Jamaican half penny depends on its condition. Such a coin is worth anything from less than a dollar to about 3 US dollars.
The British Halfpenny was first produced about 1300 AD to replace the custom of cutting Penny coins in half to achieve the required value. Many countries of the British Empire/Commonwealth also produced a Halfpenny coin for their respective currencies. Most of those countries including Australia, Britain, New Zealand and South Africa, to mention a few, produced a Halfpenny coin in 1942. The US has never minted half penny coins. The US made half cents from 1793 to 1857.
Since this is a very rare date for Jamaican half pennies, it is worth $380-$645 based on the condition. Congrats on your find!
1840
There are two varieties from two mints of 1840 US half dimes and their values range from about $10 for a type 1 from Philadelphia in Good condition to $2200 for an uncirculated type 2 example from New Orleans.
An Hibernia (Irish) 1823 copper Halfpenny, circulated but still in good condition, might fetch anything from £5 to £25 GBP. An Hibernia (Irish) 1823 copper Halfpenny (Proof FDC), uncirculated and in absolute mint condition could fetch up to £200 GBP. A reputable coin dealer will be able to give a more accurate valuation.
There were was no Australian 1956 Halfpenny minted.
The last Australian Halfpenny was minted in 1964.
The last Australian Halfpenny was issued in 1964.
The last Australian Halfpenny was minted in 1964.
There was no 1948 New Zealand Halfpenny minted.
Any Halfpenny coins circulating in Gibraltar in 1917 would have been British Halfpenny coins.
The Royal Australian Mint produced no Australian Halfpenny coins from 1956 to 1958 inclusive.
The Halfpenny has never been minted in silver. If you have a "silver" Halfpenny, it is possibly because somebody has silver plated it. Modified coins have no collector value. For future reference, please provide a year.
An Eireann (Irish) 1928 bronze Halfpenny (pig), uncirculated and in absolute mint condition could fetch up to £38 GBP. If it has been circulated but still in good condition, it might fetch anything from £2 to £12 GBP. An Eireann (Irish) 1928 bronze Halfpenny (pig)(Proof FDC), uncirculated and in absolute mint condition could fetch up to £40 GBP. A reputable coin dealer will be able to give a more accurate valuation.
An Eireann (Irish) 1933 bronze Halfpenny (pig), uncirculated and in absolute mint condition could fetch up to £500 GBP. If it has been circulated but still in good condition, it might fetch anything from £6 to £65 GBP. An Eireann (Irish) 1933 bronze Halfpenny (pig)(Proof FDC), uncirculated and in absolute mint condition could fetch up to £500 GBP. A reputable coin dealer will be able to give a more accurate valuation.
An Eire (Irish) 1939 bronze Halfpenny (pig), uncirculated and in absolute mint condition could fetch up to £175 GBP. If it has been circulated but still in good condition, it might fetch anything from £3 to £35 GBP. An Eire (Irish) 1939 bronze Halfpenny (pig)(Proof FDC), uncirculated and in absolute mint condition could fetch up to £850 GBP. A reputable coin dealer will be able to give a more accurate valuation.