There's Alta's Cafe [1] near the Rainey street end of the river. That's just about the only one, however. TBH - since you seem to know the area - what do you think about a coffee stand under the 1st street bridge? [2]
I say don't ruin the trails with business. There is something to be said for the absence of someone trying to sell you something. Enjoy some nature in the city, there isn't much of it.
[1] https://www.yelp.com/biz/altas-cafe-austin
[2] https://goo.gl/maps/FALgvtUESnu