Richard and Estelle appear in the 1930 and 1920 censuses living in Pittsburgh.
Richard is listed with his parents Richard and Cecelia in the 1910 census of Pittsburgh. According to the 1900 census Richard Sr was born Sept 1876 and Cecelia was born Aug 1877. They were married 2 years. Living with them is his brother Joe, born July 1878.
The 1880 census of Pittsburgh shows a Richard Connelly 3 and brother Joseph 2 as the children of William and Julia, both born in Ireland.
Later census records show William was born Feb 1850 in Ireland and immigrated ca 1872. Julia was born Sept 1851 in Ireland and immigrated ca 1873. They were married ca 1876. The 1920 census shows Julia as a widow.
Richard Denis Connolly's WWI draft card shows he was born Sept 29, 1876.
Some of these records you can look at for free at beta.familysearch.org and Ancestry.com. For those you cannot see for free I suggest checking with your local libraries to see if they have Ancestry or Heritage Quest.
Assuming they died in Pennsylvania I suggest getting Richard and Cecilia's death certificates from the PA Dept of Health. They should have their parents' names. Check with the Western Pennsylvania Genealogical Society and Historical Society of Western Pennsylvania to see if they can help you find obituaries and burial places. If they were Catholic check with the Pittsburgh Diocese archives for what they may have on them.
William and Julia just might be buried in the same cemetery as some of the others.