You can make duah as much as you can . There is nothing specific about this , only in the last ten days we are instructed to say:
Allahumma innaka `afuwwun tuhibbul `afwa fa`fu `annee
Aisha, may Allah be pleased with her, said: I asked the Messenger of Allah: ‘O Messenger of Allah, if I know what night is the night of Qadr, what should I say during it?’
He (The Prophet salla Allahu alahi wa sallam ) said:
‘Say: O Allah, You are pardoning and You love to pardon, so pardon me.’
Allahumma innaka `afuwwun tuhibbul `afwa fa`fu `annee
“(Ahmad, Ibn Majah, and Tirmidhi).