The Irish Traditional Music Archive catalogue lists a copy of Shiel's Love Songs which they attribute to John Sheil[sic]. None of the listed contents look like the 'The Fair Maid of Screen' mentioned in 'Greenmount Smiling Anne', but for what it is worth I'll add them here:-

Mary the Star of Cullfure [song: words only] (air: The Shamrock Shore) -- Nice Little Neat Little Factory Maid, The [song: words only] (air: The Unfortunate Rake) -- Garristown Jack [song: words only] (air: Paddy O'Carroll) -- Brilliant Bright Torch of Ardee, The [song: words only] (air: The Fair Colleen Dhue) -- Posey of Stabannon, The [song: words only] (air: The Coronation) -- Young Henry of Sweet Ravensdale [song: words only] (air: The Bonny Sweet Banks of Finn) -- Flower of Beamore, The [song: words only] (air: The Rose of Ardee) -- Bellewstown Hill [song: words only]