I am looking for a way to provide quick responses for the users during a dialog where the user can quickly respond by selecting one of the provided responses.
After searching I found this for Dialogflow ES but unfortunately I am using CX.
For the Dialogflow Messenger you can define custom payloads to add buttons or suggestions chips (which actually sounds exactly what I need) but I have no clue how to actually provide a response which acts as an intend for the dialog.
As I mentioned in comment section, Dialogflow have a 3 Editions - Trial, ES and CX
Trial:
A free edition that provides most of the features of the standard ES agent type.
ES:
The Dialogflow Essentials (ES) Edition is a pay-as-you-go edition that provides the standard ES agent type.
CX:
The Dialogflow Customer Experience (CX) Edition is a pay-as-you-go edition that provides the advanced CX agent type.
For more detailed comparsion, you can check artice: Dialogflow CX vs ES: A Complete Overview.
What you are looking for was mentioned in tutorial: How to Add a Rich Message Button Response to Chatbot Using Dialogflow?. You can find there that:
Dialogflow has recently released Dialogflow CX and renamed the existing version to Dialogflow ES. Rich messages including the buttons are supported in both. Read about differences in Dialogflow CX and ES here
As addition, you can read this article which might help you - Add chatbot rich messages using Dialogflow Fulfillment or check another stackoverflow thread here.