I've been tossing this idea around now for the last five years or so. But, with the priest shortage that we've been having throughout the entire world (with some exceptions), it is more or less something that seems unlikely to occur, at least anytime soon.
We have Perpetual Adoration Chapels, in which you can visit Jesus in the Blessed Sacrament of the Eucharist 24 hours a day, 7 days a week, 363 days a year (since He's generally taken out on Good Friday and returns Easter Sunday). The whole idea behind perpetual is that it is always ongoing.
I think Perpetual Confession Chapels, in which a priest is always on hand to hear confessions, would be a huge blessing to the Church. With the priest shortage, confession times can be lacking. I'm lucky enough to have several priests in the area who hear confessions on a regular basis, but, there are many who are not this fortunate.
I've seen at many parishes that there is no posted times for confession. This is a great tragedy when a Sacrament of the Church is not made readily available. I've also seen some of the oddest time frames for some confession times (this goes all over the place, I've seen confession times posted that take place during the work day (in which this is the ONLY time it takes place in a week)). This makes it difficult to go to confession, especially when needed.
The other problem is that at the average parish, confession times are either Saturday morning or afternoon. This is good, I'm not complaining about this, but for those who do commit a mortal sin earlier in the week (and would like to confess so they don't risk eternal damnation), waiting all week until Saturday feels a bit...risky.
Yes, you can call the priest and schedule an appointment. But, that can ruin the anonymous nature of the confessional (for those who wish to remain private). Now, if you do need to go, I do encourage you to call and schedule an appointment with Father.
With the importance of confession and getting us sinners back into the state of grace, it would be a huge blessing to know that we don't have to wait until Saturday to go, and we can easily go down to the chapel at anytime. Even if its in the middle of the night, without an appointment and can go completely anonymous.
One way we could implement this now (which would probably be a stretch, but doable) is to have a location in each diocese to where the perpetual confession chapel will be. Each priest with the diocese will have rotating shifts (not sure how long the shifts would be, but those are details that can be ironed out later). If this became incredibly popular, we could double up the shifts (multiple priests) or add other locations within the diocese.
Imagine the spiritual health that the Church would have throughout the world if this was implemented. Perpetual Adoration greatly increases the faith at the parish that it is implemented in. Perpetual Confession would do the exact same thing.