Mention that you are looking for sponsors within the app (include a link that shows your numbers and how to get in touch).

Consider affiliate links (could be text or images).

There's also the option of having a way for people to give you money (a paypal link) if they are enjoying it.

I know one newsletter which has a section dedicated to just their sponsors, allows people to pay to be included in other sections, and has a website and email sponsor (two separate sponsors).