A helpful publication that includes early Delaware information is:
Scott, Kenneth, and Janet Clarke. Abstracts from the Pennsylvania Gazette, 1748-1755. Baltimore, Maryland: Genealogical Publishing, 1977. (Family History Library book 974.811 B38sa.) During this period, Delaware had no newspaper, so the Pennsylvania Gazette gave extensive coverage to what is now Delaware. The volumes contain one- to two-line news items with names and dates and include an index.
Delaware's first regular newspaper, the Delaware Gazette, began publication in 1785 at Wilmington. Major collections of Delaware newspapers are found at the Historical Society of Delaware, American Antiquarian Society, Library of Congress, and Historical Society of Pennsylvania.
The "Delaware Index," an index to the Wilmington, Delaware News Journal and miscellaneous books and pamphlets from 1871 to the present, is available at The Wilmington Institute Library, Tenth and Market Street, Dover, Delaware 19801; telephone: 302-571-7400; fax: 302-654-9132.
The Family Surname File of the Historical Society of Delaware includes an index to newspaper obituaries from about 1850-1960. For more details see the "Genealogy" section.
Some helpful abstracts are:
Richards, Mary Fallon. Deaths From the Delaware Gazette, 1854-59, 61-64. Wilmington, Delaware: Delaware Genealogical Society, 1995. (Family History Library book 975.1 V28d.) You can use this work to supplement and authenticate death information you find in census records and Delaware vital records sources created before 1913. The information has been abstracted from death and marriage notices, local news columns, estate references by the Registrar's office, and executor/trustee sales.
Richards, Mary Fallon. Marriages From the Delaware Gazette, 1854-59, 61-64. Wilmington, Delaware: Delaware Genealogical Society, 1996. (Family History Library book 975.1 V28d v.2.) You can use this work to supplement and authenticate marriage information taken from census records and Delaware vital records sources created before 1913. The information has been abstracted from death and marriage notices, local news columns, estate references by the Registrar's office, and executor/trustee sales. It also includes a list of ministers (with church locations) whose names appear in Delaware Gazette marriage notices, 1854- 64.
Wright, Edward F. Delaware Newspaper Abstracts, 1786-1795. Silver Springs, Maryland: Family Line Publications, 1984. (Family History Library book 975.1 B3w.) This publication abstracts major Delaware newspapers except for the American Antiquarian Society collection. Indexed.
Frazier, Margaret Mendenhall. Delaware Advertiser, 1827-1831, Genealogical Extracts. Newhall, California: Carl Boyer, 3rd, 1987. (Family History Library book 975.1 B3f.) This newspaper was a four-page weekly published every Thursday. Information extracted includes deaths, marriages, legal notices, and taxpayers. Indexed.
Delaware Newspaper Project: http://www2.lib.udel.edu/delnews/