I am Jewish and dating a woman who is considering conversion to Judaism. I'd be so happy if she did convert, but I don't want to seem like I'm forcing her to convert. How can I best support her without coercing her?
In a way, you've answered your own question: Support, not coercion. No one should convert out of coercion, and no rabbi should be involved in such.
When I send a prospective Jew by choice to an Introduction to Judaism class, if there is a Jewish partner involved I push hard to have the Jewish person join the class as well in support of their partner. Attending synagogue and bringing Jewish rituals into personal life as much as possible also is a way to support their partner. If the Jewish partner can't go to class, then s/he should at least be willing and able to discuss the classes and support the study ― even read some of the books.
Years ago, Egon Mayer, a Queens College sociologist and maven on conversion, spoke at my congregation and said that the main reason given by people for not converting is that they were never asked. So the Jewish partner should indicate that honest conversion would be very important to them, as would a Jewish wedding.