Apple does not make it possible to download pre-Sierra installers either via their website or App Store.
That's not quite right. Any OS X version that you've "purchased" (i.e. downloaded from the App Store) should be re-downloadable by going to the Purchased tab. In your case, you won't see Yosemite there because your Mac shipped with it, but you should see El Capitan.
Just click on the
Download button. (Instructions for saving the installer without installing the OS are readily googleable.) If the button is dimmed and reads
Downloaded instead, that means you've already got a copy of the installer somewhere.
