In suttacentral Daya is put almost like if it’s meaning Dana apart from fee. (a gift, donation; share, fee)
So I think it should be in place of fee. Friendly gesture. Because the following
But here it says
Compassion:
One should behave like his own self, towards others, his own relations and friends, him who envies him, and even his enemy. This is called Daya.
— Atri Samhita, Translated by MN Dutt
Any sutta reference where Daya is used in that meaning?
And for Dana
Charity:
Even with limited income, something should be given away daily with care and liberal spirit. This is called Dana
I suspect different interpretations but probably the old meanings got lost with time.
I am not entirely sure what it is that you want replaced with what but daya traditionally has meaning along the lines of compassion, kindness, pity, or mercy, depending on the context. Dana on the other hand is always associated with giving, charity, gift, donation, benefaction etc. If you stop yourself from killing someone (even though you easily could), you are showing daya and giving them dana of life.
Offhand I don’t know pali words for that but in current north Indian languages the closest words would be dua, āshirvād, or if someone is bestowing you with an exceptional (supernormal) blessing then it would be vardān. I don’t know if this helps.