Business cards for a postdoc: what affiliation?
The cards should list the employee's current place of employment, just like business cards for any other job. The only thing that should be different for a postdoc is that you should make sure the image file for the cards is easy to update when she gets a new job.
Business cards themselves are not a terribly common practice for postdocs in my field (some combination of biology, physics, others). I think I've been handed one at a conference maybe once or twice.
I don't have a simple answer, but here are the factors I'd think about:
Don't put her institutional email on it, because it will expire quickly once she leaves - it's better to use a [professional-sounding] external one. (Similar factors can apply to university websites, but they've been better in my experience.)
Consider how likely it is that she'll use the entire run of 100 or so cards in the next year, before having to change the affiliation.
I would probably not list an affiliation that isn't current on a business card. She may, however, list that affiliation in the conference program if she's talking about her dissertation work - or it may be obvious from her coauthors.
Will having no visible affiliation make her look like a crackpot? This depends on the culture of the field. Probably there are no strange unaffiliated people presenting their Unified Theory of Russian Literature at the MLA Convention, but in physics, it's an issue.
First, is the University sending her to this conference? (i.e. paying for her attendance, flight, hotel, etc...) If so, I would consider her a representative of the University and her business card should reflect it, email address and name of the institution. If the work presented was performed at a different University, then this should be evident in her presentation.
Second, When I was at an R1 University and wanted business cards for a conference, they had a few approved templates that I could choose from and then they printed them for me. Their might be rules about using a "non-approved" design. Check with her University.
Lastly, keep in mind that the quality of her research and presentation is much more important than the branding on her business card.