Gratitude in Islam flows in two directions — thanking Allah for His blessings and invoking His blessing upon people. These duas cover both: congratulating others and honouring parents.
1. Congratulations / Blessings
بَارَكَ اللَّهُ لَكَ
Baarakallaahu lak.
May Allah bless you.
Source: Abu Dawud 2130
2. My Lord, have mercy on them both as they raised me when I was small.
رَبِّ ارْحَمْهُمَا كَمَا رَبَّيَانِي صَغِيرًا
Rabbir-hamhuma kama rabbayani saghira
My Lord, have mercy on them both as they raised me when I was small.