I really appreciate your question because sentimental comedy is a term I was not familiar with. I happened upon an essay by Oliver Goldsmith (British playwright of Restoration Comedy fame) from 1773, in which he details the distinguishing elements of sentimental comedy:
[V]irtues of private life are exhibited, rather than vices exposed, and the distress rather than the faults of mankind make our interest in the piece. In these plays almost all the characters are good, and exceedingly generous; they are lavish enough of their 'tin' money on the stage, and, though they want humor, have abundance of sentiment and feeling. If they happen to have faults or foibles, the spectator is taught not only to pardon, but to applaud them, in consideration of the goodness of their hearts; so that folly, instead of being ridiculed, is commended, and the comedy aims at touching our passions without the power of being truly pathetic.
I have included a link to the essay by Goldsmith, in which he goes on to compare the sentimental comedy with what he calls "laughing" or truly humorous comedies.
Sentimental Drama - both sentimental tragedy and comedy - finds its origin in the reaction against the obscenity of the Restoration Comedy of Manners. The obscenity in the Restoration Comedy of Manners was itself due to its being a reaction against the Puritanism of the Commonwealth of Oliver Cromwell.
"Sentiment" would of course mean 'excess of emotion.' Sentimental drama was characterized by scenes which were meant to evoke excessive pity - a helpless widow with many children, a reconciliation scene between a repentant son and a magnanimous father, a reformed husband being reunited with his wife.
Richard Steele's (1672-1729) "The Conscious Lovers" (1722) is a typical example of Sentimental Comedy whereas George Lillo's (1693-1739) "The London Merchant" (1731) is a typical example of a Sentimental Tragedy.
For a certain period of time Sentimental Drama was popular, but soon people got tired of it and the Comedy of Manners which had become unpopular because of the advent of the Sentimental Drama was revived in the 18th century by Goldsmith (1728-74) and Sheridan (1751-1816). Both these dramatists took care to keep their plays free of the obscenity which was the reason for the Restoration Comedy of Manners becoming unpopular. The 18th Century Comedy of Manners is different from the Restoration Comedy of Manners in that it is not obscene. It is a sanitized version of the obscene Restoration Comedy of Manners. After Sheridan and Goldsmith there was no one to continue the tradition of the Comedy of Manners.
The tradition of the Comedy of Manners had to wait till the arrival on the scene of Oscar Wilde (1854-1900) to be revived again. The plays of Oscar Wilde follow all the conventions of the traditional Comedy of Manners plays. They are famous for their intricate plots and Wilde's unique brand of epigrammatic wit.
Wilde's plays belong to the Comedy of Manners genre.
THEY ARE ANTI SENTIMENTAL DRAMA.
Melodrama (Greek, melos - music and French, drame - drama) is a particular type of drama which is characterised by extreme exaggeration. Melodrama became popular only from the 18th century onwards and it was always accompanied by orchestral music or song.
The Comedy of Manners became popular as early as the Restoration in 1660. The Sentimental Comedy which has melodramatic - exaggerated and difficult to accept as genuine and sincere - scenes and characters originated only after 1700. Sentimental Drama has no orchestral musical accompaniment.