You didn’t say what trim level or year your Civic is, but most Civics come off the factory line with a battery made just for Honda. To get a battery labeled a genuine Honda part, you may have to order one through your local Honda dealer, but you can check around online as well.
Your Civic probably takes a 51-R. You can check this by inputting your Civic’s precise specs into a battery database (at a battery retailer). The 51-R group typically are made as either AGM or SLA batteries.
MORE: What you should know about the Honda Civic battery draining problem