This is a close call. Dumbledore "ordered" Snape to kill him before the events of HBP, Chapter 3, and the Unbreakable Vow takes place in HBP, Chapter 2. Thus I can't really answer your question; I can only explain what indications we have of when the "order to kill" took place.
In The Prince's Tale (Chapter 33 of DH) we see Snape's memory of the day on which Dumbledore fooled about with the Resurrection Stone, almost killing himself:
"Why," said Snape, without preamble, "why did you put on that ring? It carries a curse, surely you realized that. Why even touch it?"
Marvolo Gaunt's ring lay on the desk before Dumbledore. It was cracked; the sword of Gryffindor lay beside it.
A bit later, Snape asks Dumbledore if he intends to let Draco kill him, to which Dumbledore replies:
Certainly not. You must kill me.
From HBP (Chapter 3) we know that this happened before the beginning of Harry's 6th year. When Dumbledore comes to the Dursleys to fetch him,
Harry saw that his hand was blackened and shrivelled; it looked as though his flesh had been burned away.
Thus, Dumbledore requested Snape to kill him before he fetched Harry from the Dursleys, and the Unbreakable Vow was also performed before that date.