A little googling turned up this list of DE newspapers.
http://www.usnpl.com/denews.php Not sure which are in your county but you should be.
Requirement:
“Publication of your intent: You must publish your full name, your home address and indicate your intent to make application for a Delaware CCDW in a newspaper, published in your county, that has a circulation of at least 35 percent of the population in your ZIP code. Check your local newspapers if they meet this qualification — prices for a legal notice can run from $15-$75 depending on the publication. The notice must run at least 10 days before you file your application and the newspaper will send you a notarized letter that your ad was run.”
Sphinx, you can also call your office of the Prothonotary and ask them and they will tell you all the acceptable newspapers in your county.