I am also researching (though not vigorously) Richard Constantine's line in Baltimore. This is my cousin's ancestry, not mine. She is related to Hester Contantine who wed George C. Ness in 1857. Hester was the daughter of Richard Constantine and Leah/Lena Burck, who wed in 1825. Richard, I believe, was the son of Richard & Elizabeth.
Since this isn't my family, I don't have much. This is what I do have:
Burial at St. Paul's P.E. Church- (Baltimore) Ruth Constantine, dau of Richard1803
Loudon Park Cemetery- lotholder- Richard Constantine
Marriage- Patrick Constantine to Anne Bond 29 Sep 1760 (St. Thomas Parish, Baltimore County)
Six burials from St. Patrick's Roman Catholic Church in Baltimore with the name Constantine ranging from 1883 to 1899.
Deed/ assignment in Baltimore naming Richard of Richard Constantine dated 1841 for a lotat ES Cathedral Street. (I don't have the actual copy, just this from an index.) The other party was listed as John Moorehead and others.Book TK 308 page 317.
A deed for Edward Constantine & others in April 1845 and another deed for Daniel Constantine March 1847. Again no actual deeds, just a name index.
I'm sure you have the will for Richard Constantine in 1832, probated 1833, naming Elizabeth sole executrix.
This is all I have except the census records which I'm sure you already have.