There's a woman we have been sharing the gospel who wants to be baptized—but she's in the hospital and no tanks are on-site. (It's unlikely she'll ever leave the hospital.) Have you had any experience with this sort of issue?

Yes, I've witnessed two approaches to this, although I can imagine a third.

As much as it bothers me, some brothers have simply poured water on the hospital patient. Of course this is not strictly speaking immersion, but perhaps it is the best that can be done in such situations. I'm one man who was expected to die in the hospital. The brothers poured water on him. He ended up recovering, and some weeks later decided that he should be immersed.

I prefer a different approach, which is to expect the patient to persuade the doctors to provide a tank or tub for baptism. If this is a last wish of the dying patient, it is easy to see some nurses or doctors being sympathetic to such a request. This exact thing has happened in our ministry in the past.

I also recall the case of a cancer patient (nearly 50 years ago) for whom to come into contact with water would be very dangerous. I think the issue was that the pain could have been so intense it would stop her heart. She was wrapped up in plastic and then immersed in the church baptistry, so that no moisture touched her skin.

A third answer, which seems to date to the church fathers, is to consider the intent or trajectory of the person's life. A number of mean and women were martyred for the faith before they could be baptized. Others were even martyred for the faith on the way to baptism! In the case of martyrs, this was sometimes called "the baptism of blood."

I wish I could give more direct advice, but I am probably too far removed from the situation. This is the decision of the one coming to faith. It's easy to imagine different opinions about this matter, which is one reason I presented three answers. Ultimately we are left to trust in the Lord's justice and mercy.