To approach the opposing point of view of your topic, you may need to think about what you're looking for with a bit more nuance. For many topics, your opposing viewpoint article won't argue that the issue you've selected is totally invalid or isn't a real issue.  Instead, look for articles with a viewpoint on a specific proposed resolution to an issue or a specific policy related to it.  

For example, let's say you're researching school bullying and during your research, you noticed some articles in search results discussing the failure or insufficiency of school bullying policies. Instead of trying to find articles talking about how school bullying isn't an issue and doesn't exist (which to find a credible source, could be quite difficult), the counter-argument article you choose for the assignment could focus on why or why not a specific policy is effective, like if mandatory school-based bullying education programs are effective or not. 

Issues & Controversies is an excellent database to find pro/con style reports, news articles about national topics, editiorials, and more. This should be a first stop in researching for your persuasive essay!

Below is a screen capture of a search in Issues & Controversies displaying opposing viewpoints:

After becoming familiar with the pro and con points of view of your topic, continue your research in Credo Reference and Gale eBooks.

Credo Reference offers over 2,000,000 reference entries from all the major academic subject areas to offer a great starting point for your research! Tons of images, audio files, videos and full text articles.

Below is a screen capture of a search within Credo Reference. Notice that this database displays additional Library database search results in addition to the main search results:

 In Gale eBooks, search through over 1,200 reference e-books on business, health, law, and more. Result lists highlight entries from encyclopedias and other reference books.