You could probably do something along these lines, provided that you've uploaded the appropriately named files to your /assets folder:
{% capture w %}{{ 'now' | date: '%w' }}{% endcapture %}
<img src="{{ 'banner-w.jpg' | replace: 'w', w | asset_url }}">
Which would return:
<img src="//cdn.shopify.com/s/files/1/0699/1389/t/1/assets/banner0.jpg?9"> on Sunday, "banner1.jpg" on Monday, etc.
That will return the current date / time on the server, so it's possible that the end user might see it sooner or later than they should. If you need it to be accurate on the user end you'd need to implement a JavaScript solution.