On November 14, 1791, a committee was formed "to prepare and bring in...a bill to alter, change, and explain the constitution and form of government of this state in certain particulars therein mentioned," whose members were:
William Pinkney, Harford County
Gabriel Duvall, Annapolis
William Craik, Charles County
William Clagett, Washington County
John Francis Mercer, Anne Arundel County
John Griffith Worthington, Anne Arundel County
James Tilghman, Talbot County

See p. 13, Votes and Proceedings of the House of Delegates, November Session, 1791

On December 26, 1791, Gabriel Duvall introduced a long list of bills that were "read for the first time and ordered to lie on the table," having to do with changing the constitution.  The bills were:
1)  A bill entitled, An act to prohibit members of congress, or persons in office under the United States from being eligible as members of the legislature or council, or holding offices in this state
2)  A bill entitled, An act to repeal the twenty-seventh section of the constitution and form of government
3)  A bill, entitled, An act to repeal the forty-fifth section of the constitution and form of government
4)  A bill, entitled, An act prescribing the oath of a judge, and the oath or affirmation of the clerk, of the elections
5)  A bill, entitled, An act allowing citizens, conscientiously scrupulous of taking an oath in any cafe, to be members of the legislature, or electors of the senate
6)  A bill, entitled, An act respecting negroes and mulattos
7)  A bill, entitled, An act respecting naturalized foreigners
8)  A bill, entitled, An act an act to explain the qualification of residence required in the constitution and form of government
9)  A bill, entitled, An act to repeal all the oaths required by the constitution and form of government with certain exceptions, and to require an oath to preserve and support the constitution of this state
10)  A bill, entitled, An act prohibiting the incorporating any place, or the erecting a new county [word illegible] the privilege of delegates, unless they contain a limited number of voters
11)  A bill, entitled, An act respecting the appointment of the register in chancery, and the other offices therin named
12)  A bill, entitled, An act to abolish informations in court of common law
13)  A bill, entitled, An act respecting the holding of office by members of the general assembly
14)  A bill, entitled, An act to explain and amend the constitution and form of government as to the election of electors to the senate
15)  A bill, entitled, An act to alter and amend the constitution and form of government as to the filling of vacancies in the senate; and to allow the senate to amend money bills
16)  A bill, entitled, An act to alter and amend the constitution and form of government as to the election of members of the house of delegates
17)  A bill, entitled, An act to alter and amend the constitution and form of government as to the elections of governor
18)  A bill, entitled, An act to alter and amend the constitution and form of government as to the council
19)  A bill, entitled, An act directing the mode of appointing the officers herein mentioned
20)  A bill, entitled, An act to repeal the forty-second section of the constitution and form of government
21)  A bill, entitled, An act concerning sheriffs
22)  A bill, entitled, An act to secure the trial by jury in civil cases
23)  A bill, entitled, An act to repeal such parts of the constitution and form of government as require the qualification of property for the governor, and others
24)  A bill, entitled, An act to prohibit the calling of conventions to alter the constitution and form of government, unless with the consent of the legislature
(See 1791 Votes and Proceedings, pp. 116-117)

The first bill, a bill entitled, An act to prohibit members of congress, or persons in office under the United States from being eligible as members of the legislature or council, or holding offices in this state  was read a second time "by special order," passed, and sent to the Senate by the clerk.  This was the only bill out of the list that passed, becoming ch. 80, Acts of 1791.

On motion, it was ordered that the "several bills proposed by the committee appointed to consider what alterations of the constitution and form of government are necessary, be referred to the consideration of the next session of assembly, and that the same be published in the Maryland Gazette, the Baltimore Journal, the Frederick and Georgetown papers, and the Maryland Herald.

The first bill probably arose from the fact that Charles Carroll of Carrollton and John Henry were both in the U.S. Senate in 1791 at the same time that they were running for the state senate.  When Carroll was elected to the state senate on September 23, 1791, "agitation" on the issue "intensified" which probably contributed to the introduction and subsequent passage of the bill (J. R. Heller III, "Democracy in Maryland 1790-1810," senior thesis, Princeton University, 1959, pp.18-19).
Heller cites the Maryland Journal and Baltimore Advertiser on 15 September 1791, but I checked that date as well as the days following the September 23 election and saw no mention of the issue.  The Maryland Gazette did not report on Carroll's election in the issue immediately following it (September 29, 1791), nor in the following issue (October 6, 1791).

None of the bills were reported in the Maryland Gazette in the first issue after Christmas, which was December 29, 1791.  The only report on the House of Delegates in that issue is a reprint of the vote condemning a memorial of the Maryland Society for promoting the Abolition of Slavery, and the Relief of Free Negroes, and others, unlawfully held in Bondage, as "indecent, illiberal, and highly reprehensible, and moreover is as untrue as it is illiberal."  Apparently the Society caused quite a stir among the delegates during that session, as it is mentioned disparagingly several times in the Votes and Proceedings before Christmas.  I am wondering if some of the delegates felt threatened by the Society to the point where they would rewrite the constitution specifically prohibiting negros and mulattos from voting and holding office.

There was a special session of the House of Delegates held in April, 1792, but Duvall's long list of bills were not taken up.  At the next regular session of November 1792, the bill to confirm the act passed in 1791 to prohibit members of congress, or persons in office under the United States from being eligible as members of the legislature or council, or holding offices in this state was passed.   On November 15, 1792, Duvall called for a list of yeas and nays on the question of whether the House would take into consideration the next day the several bills for amending and altering the constitution reported by the committee of November session last.  Not only did they vote to not consider the bills the next day, but they voted to not consider the bills at all that session.  (See list of yeas and nays in 1792 Votes and Proceedings, p. 16)   I checked the next two issues of the Maryland Gazette after November 15, 1792 to see if anything was written about Duvall's proposals.  There was an extensive editorial from the "censor" to the members of the General Assembly on the issue of duel officeholding (the author believing a person should be able to hold both state and federal office at the same time, and to prohibit that would be against the U.S. constitution), but otherwise nothing specifically on Duvall's list or a new constitution.