The title of this post is slightly disingenuous; Jane Austen doesn’t actually write the stage of prayer in which God consoles the soul with “sweet feelings,” but this passage of Sense and Sensibility seems to me a excellent likeness of what seems to be meant by such expressions:
Edward was now fixed at the cottage at least for a week;—for whatever other claims might be made on him, it was impossible that less than a week should be given up to the enjoyment of Elinor’s company, or suffice to say half that was to be said of the past, the present, and the future;—for though a very few hours spent in the hard labor of incessant talking will despatch more subjects than can really be in common between any two rational creatures, yet with lovers it is different. Between THEM no subject is finished, no communication is even made, till it has been made at least twenty times over.
It is recounted of Msgr. Ronald Knox that immediately after his conversion he was receiving many sensible consolations, and that sometimes he would run on his way to Church in his impatience to pray before the Blessed Sacrament.