Do I need an SD card to add apps to an Advent Amico Android Tablet?
You could try emailing them to yourself or downloading them from somewhere (Dropbox public link or a web host of some sort). On most (if not all?) devices you can just launch an .apk after it's been downloaded and it will open with the application installer.

You'd most likely also need to allow "Unknown Sources" for this to work, which should be found in the settings menu under Settings-&gt;Applications-&gt;Unknown sources.