I don’t believe it is possible (or appropriate) to use Alerts this way.
Modals are the way to go but at the moment they appear just like full screen pages with maybe a different default transition and stacking than pages (i.e there’s not much visible difference between modals and pages). You may have to wait until Inset Modals are introduced in Beta7 like I am…
…if you want to achieve something like an Alert but with extra customisation ability.
You can add padding to the existing modal functionality to make it look like it’s inset but it’s a bit of a hacky approach: