Is it permissible to publish a call for charity by placing a small amount of money in a special box for every sin a Muslim commits, and then donating the contents of the box?

There is no harm in a servant giving charity whenever they commit a sin, for this is following a bad deed with a good one. It is better not to specify a particular act of worship but rather to perform a good deed in general after a sin. Inviting people to do so is permissible, as it is an invitation to what Allah has legislated. However, there is no need to specify giving charity only when the moneybox is full. Rather, it is better to seek what is most beneficial. Perhaps expediting each act of charity is better, or saving the money until the charity is of significant value.