I think that any prayer for another person (living or deceased) is an act of mercy. However, I’m not sure what you mean by “count as your act of mercy.” Acting mercifully toward others — by actions, kind words, and prayers — should be a way of life, and should happen dozens of times of day. Here is an excerpt from Faustina’s diary (#163, prayer for the virtue of mercy) that shows the spirit of this requirement:
O Most Holy Trinity! As many times as I breathe, as many times as my heart beats, as many times as my blood pulsates through my body, so many thousand times do I want to glorify Your mercy.
I want to be completely transformed into Your mercy and to be Your living reflection, O Lord. May the greatest of all Your attributes, that of Your unfathomable mercy, come to pass through my heart and soul to my neighbor.
Help me, O Lord, that my eyes may be merciful, so that I may never suspect or judge from appearances, but look for what is beautiful in my neighbor’s souls and come to their rescue.
Help me, that my ears might be merciful, so that I might give heed to my neighbor’s needs and not be indifferent to their pains and moanings.
Help me, O Lord, that my tongue may be merciful, so that I may never speak negatively of my neighbor, but have a word of comfort and forgiveness for all.
Help me, O Lord, that my hands may be merciful and filled with good deeds, so that I may do only good to my neighbors and take upon myself the more difficult and toilsome tasks.
Help me, O Lord, that my feet may be merciful, so that I may hurry to assist my neighbor, overcoming my own fatigue and weariness. My true rest is in the service of my neighbor.
Help me, O Lord, that my heart may be merciful, so that I myself will feel all the sufferings of my neighbor. I will refuse my heart to no one. I will be sincere even with those who I know will abuse my kindness. And I will lock myself up in the most merciful heart of Jesus. I will bear my own sufferings in silence. May Your mercy, Lord, rest upon me.
You Yourself command me to exercise the three degrees of mercy. The first: the act of mercy, of whatever kind. The second: the word of mercy — if I cannot carry out a work of mercy, I will assist by my words. The thrid prayer — if I cannot show mercy by deeds or words, I can always do so by prayer. My prayer reaches out even there where I cannot reach out physically.
O my Jesus, transform me into Yourself, for ou can do all things.