Have you found John and/or Peter on the 1901/1911 Irish Census ?
If John was born in the City of Dublin then the two likely registration districts are Dublin North and Dublin South - but note that these also cover areas outside the city. Assuming the year of birth is accurate then these are the possible matches on the BMD Index :
Name: John Joseph Smith
Registration District: Dublin North
Event Type: Birth
Quarter and Year: Apr - Jun 1882
Volume: 2 / Page: 511
Name: John Laurence Smith
Registration District: Dublin North
Event Type: Birth
Quarter and Year: Apr-Jun 1882
Volume: 2 / Page: 547
Name: John Smith
Registration District: Dublin South
Event Type: Birth
Quarter and Year: Apr-Jun 1882
Volume: 2 / Page: 663
Name: John Harold Smythe
Registration District: Dublin South
Event Type: Birth
Quarter and Year: Apr-Jun 1882
Volume: 2 / page : 674
Note that years of birth reported in later records are not always accurate... so you may need to allow a couple of years either way when searching...
You can also check RC baptism records for many parishes in Dublin City on
www.irishgenealogy.ie I dont see any sign of a John Smyth with father Peter during 1882, but further records are due later in the year
Shane