To remember the machatzis hashekel, the custom is to give three half denomination coins to tzedakah around Purim time. In places like the US where half denomination coins take some work to get, a shul usually gets several sets and people "buy" them and donate them back.
Based on this answer, it may be preferable to use a coin that contains silver, which in the US means older half dollars. Coin collecting websites (example) say that those are worth a lot more than 50 cents. The Franklin half dollar, which stopped production in 1963, is apparently worth $5.73, and older half dollars are worth a lot more.
According to the Rambam, this is very similar to the situation that led to the enactment of the kalbon. A whole shekel (aka sela) coin is sometimes worth more than a half shekel coin, so two people who want to fulfill their obligation together with a single sela have to pay the difference in price, known as a kalbon.
If a shul gets older half dollars and you buy them from the shul, do you have to give a kalbon? Do the same parameters apply (e.g. kohanim and women are exempt)?