For whatever reason, Quotes are immensely popular and one of the highest searched terms on Search Engines.
Now, because there are countless Apps already, you'd definitely need to monetize with advertising or perhaps implementing something that the user could personalize the quotes with. Pictures, backgrounds, etc

Everyone likes or needs quotes at one point or another of their pro/ personal life.

My experience - I develop apps for people like you, and own this App development company www.agicent.com, and here's my take specific to your question:-

There is a potential, but you need to offer "either the same thing in different way" or "different thing in different/ same way" w.r.t what's already there in the market. It could be some associated new features along with quotes, or something more personalized offerings (based on mood etc), and ofcourse with some "FRESH" content. May be you allow users to put their quotes also, and publish to community for vote up/ down etc.

Also,don't miss the most important aspect (that many in this business miss) of rolling out new features frequently, and engage customer proactively (by fb groups, notifications, analysing their data and suggesting them something, allowing them to contribute to the app by blog/ comments etc). Basically, a sense of "community" needs to be achieved, and then you can figure out many revenue intersections (when you've great no. of Daily Active users).

Some common revenue streams are advertisements, in-app purchases (of any premium content etc) or even 1 time fee. Some little uncommon could be gaining sponsorship from business related to what you offer (for example book publishers, therapy providers etc, whoseover thinks their target user group uses your app).

I'm glad to discuss this at length with you, and brainstorm together should you feel so.