Yes, you can intercede on her behalf. You can write a letter. The recipient will see the astral component of the letter, which will convey more than your words can. Write a simple letter with the facts of the case, and the recipient will know what needs to be known.
You do not need her blood. You can use a bit of your own if you wish, since you are the one writing the letter.
Your prayer can be your own words, from your heart.
Everything has a cost, this is how nature works on every level. In such a case, the sick person owes the debt. You can offer to contribute to the alleviation of the debt, if you wish, by whatever means you wish. But be very careful: such negotiations are serious. Do not offer what you cannot pay. I recommend that you attempt to find out through dreams or visions what you can do; your Being will guide you.
A coma is a disconnection between the psyche and the body. It is similar to what happens when we dream, but is obviously stronger and more intense.
You can help the soul by reading scripture near the persons body, especially scriptures about death and dying that guide the soul. You can also recite prayers, conjurations, etc., as these will clarify the atmosphere and help the soul in turn.
“Nothing is easier than self-deceit. For what each man wishes, that he also believes.” —Demosthenes
"Do not worry; cultivate the habit of being happy." —Samael Aun Weor