I located some possible baptisms for several of the children you mentioned, in Milltown Catholic Parish. All three give residence as Rockfield - mother's name recorded on the baptism of Michael is Ellen, possibly in error...:
Michael Clifford bapt. 24th January 1887
Julia Clifford bapt. 17th July 1889
Eugene Clifford bapt. 30th August 1892
see : Clifford / Lynch baptisms (IrishGenealogy.ie)
Milltown RC parish is located to the south of the town of Tralee, and the IrishGenealogy website covers records for this parish up to about 1895, for later births etc see the civil BMD records also on IrishGenealogy.
There are several townlands named Rockfield in County Kerry - the first in Ballymacelligot civil parish located about half way between the towns of Castleisland and Tralee, and a group of three adjacent townlands Rockfield East, Rockfield West and Rockfield Middle in Kilbonnane civil parish. Based on the 1901 census return it looks like your Clifford / Lynch family lived at Rockfield East townland (placename database). Julia snr died on the 1st August 1896 (see entry 303 on image 1) from Physthis (Tuberculosis), her age was reported as 42, and residence as Rockfield, daughter Lizzie registered the death.
Looking back in time I located the civil marriage record for Stephen and Julia, they were married on the 17th February 1874 in the Catholic Chapel at Milltown Co. Kerry, Stephen gives his age as 28 (c1846) occupation farmer, and residence as Rockfield, Julia gives her age as 24 (c1850), 'daughter of a farmer', residence also Rockfield, it's the first marriage for both of them - Julia 'signed' the register with her mark.. The fathers are given as John Clifford and Patrick Lynch both farmers.
Based on the age reported by Stephen I checked for a possible baptism for him - Milltown parish has baptism records back to the 1820 but no promising matches showed up, however there was one good match in the adjacent parish of Molahiff/Aglis/Firies - it's the 6th entry on the right hand page, details as follows (firstnames given in Latin) : 9th October 1845 baptism Stephanus (Stephen) son of Joannis (John) Clifford and Elizabeth Casey, their residence appears to be Clounlara, the sponsors (godparents) were Eugene Clifford & Julia Kerrick/Kerrisk[?].
Unfortunately not much success with the search for Julia’s baptism - the only I found one that’s close by location and timeframe is a Juliana Lynch baptised Molahill parish to parents Patrick Lynch and Margaret Brosnan in August 1836, which seems a little early to be the right Julia...