We used Supplications in the morning and evening based on hadith. Can we add some other Du'a in the morning and evening like Du'a Qunut or Du'a which taught by Rasulullah PBUH to Abu Bakr Ashidiq ( Allahuma inni dholamtu nafsi dholman kathiroon ....that is said on the prayer and other Du'a?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Supplications are of two kinds. Some of them are restricted to a given time or number while some others are not restricted to a given time or number. The supplications that are restricted to some time or number such as the supplications recited at morning and evening, at entering or going out of the house and the like, and the supplications that are uttered following the prayers in a limited numbers, all such supplications should be done as reported without changing the time and without adding or increasing their numbers. Any changing in time or number is considered an innovation in Shariah.
As for the second category i.e. those are not restricted to a given time or number, they may be supplicated at any time i.e. morning and evening and without any limitation in the numbers. It is reported in Sahihani that the Prophet (Sallallahu Alaihi wa Sallam) used to supplicate Allah in all times.
The Du'a the Prophet taught AbuBaker and Du'a al-Qunoot may be supplicated at any time since they are not restricted to a given time.
Allah knows best.