Council, may, after public hearing, waive the payment of fees and the making of deposits and permit the construction of a parking cutout and authorize a variance in its location, shape or size whenever such parking cutout is to be adjacent to any premises used for municipal, park, school or church purposes upon a finding that such variance is reasonably necessary for the public convenience or welfare, and, with respect to other cutouts, when it is found that there are practical difficulties or particular hardships in the way of carrying out the strict letter of this chapter.