This question reminds us of a similar one we answered years ago regarding whether a rock collection is muktzeh.[1] We will summarize that discussion and then see how a coin collection compares.
Rocks are muktzeh because they generally do not have a use that would make them considered a kli (utensil).[2] However, if one prepares rocks before Shabbat for a given purpose or if their owner decides to use them permanently for a specific permitted purpose, they are not muktzeh.[3] Thus, rocks that are incorporated in a rock collection may not necessarily be muktzeh, as people enjoy looking at them.
In the question we considered, the rocks were on display in an arrangement that remains untouched over long periods of time. Does that turn the collection into muktzeh machmat chisaron kis, something one is careful not to use in various situations? The usual cases of muktzeh machmat chisaron kis are utensils that are meant mainly for forbidden purposes and whose permitted uses are not applicable at that time. Does this category extend to include an object whose purpose is permitted but one is careful to rarely move (e.g., wall clocks and paintings)? Rav Moshe Feinstein[4] rules that such items are not muktzeh, but Shemirat Shabbat K’Hilchata[5] maintains that they are muktzeh machmat chisaron kis.
Coins are muktzeh.[6] This is not only because their use is related to a prohibited activity (commerce), in which case their muktzeh status of kli shemelachto l’issur would be only partial.[7] Rather, coins are not considered utensils at all;[8] their value is not based on what one can actually do with them, but rather on the fact that people have decided that they are valuable to possess. However, if one uses coins as objects to be admired, then, on the basic level, they could be turned into non-muktzeh items.[9]
In some ways, a standard coin collection is more likely to not be muktzeh than a rock collection, if we are correct in assuming that the coins in the collection are meant to be handled. One often keeps such collections in books, whose pages are turned to look at one coin after another. Although they are nestled within plastic coverings, turning the pages is still considered moving the coins, as the pages and the plastic serve the coins. Therefore, in contrast to rocks in a rock collection that is not moved, the Shemirat Shabbat K’Hilchata should agree that the coins are not muktzeh unless one keeps them locked in a safe or otherwise rarely handles them. If the collection is slated for sale and the owner is careful not to use it in the meantime,[10] the coins would be muktzeh.[11] However, we understand that you are talking about a collection that is maintained for the owner’s personal interest.
A remaining issue is the Chazon Ish’s opinion. The gemara[12] states that if one attaches a stone to an article of clothing for a purpose of utility, it is permitted to move the stone along with the clothes, as long as he intended before Shabbat to use the stone for that purpose.[13] The gemara notes, however, that similar intention for that purpose would not suffice for a coin. Most understand this to apply only if the coin was not permanently set aside for the use before Shabbat.[14] Thus, if coins are permanently on display and no longer act as “money,” it would be permitted to move them. However, the Chazon Ish[15] says that coins cannot be considered as set aside for a purpose other than commerce, since they are always candidates to be used again as money. They consequently remain muktzeh.
You do not have to be concerned with the Chazon Ish’s opinion, however. First of all, we follow the majority, lenient ruling.[16] Second, the Chazon Ish’s logic seemingly does not apply to a coin collection. Since the coins involved have a special collector’s value that exceeds their value as money, there is no reason to suspect that one will revert to using them as money.