It is possible to book private parking spot. Exta cost is 15€ per day.
They do not arrange parking that I'm aware of but we rented a car and parked at the car park on Emonska Cesca which was a couple block over the river and always had places available.
As has been said parking is very limited but there are car parks outside the centre - a little walk away.
Get an answer from Allegro Hotel Ljubljana staff and past guests.