I would use a humanist sans, the contrast with anything else would be too much.
Scala Sans, for instance.

I once saw a calendar that used Futura with Centaur and I like they contrast between them.

I've had the same question. You might think Legacy Sans would work, because Ronald Arnholm modeled both sans and serif Legacy on the same Jenson original as Rogers did Centaur; However, Legacy Sans is totally out of scale with Centaur, both as a whole and as to x-height. You'd have to perform surgery to make them compatible.

Nick, didn't Bringhurst use Scala Sans in Vs 2.4 and 3.0 and of his typographic style book? Don't the modernistic touches in that font jar a bit with stately Centaur?

Centaur isn't stately at heading size, it's kinda scary, because it's not optically scaled.
Nicholas, a display face, is a more stately 'Jenson'.

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Better than Scala Sans: Seria Sans.

Have a differing opinion on the stately head. My mirror says that Centaur is the stateliest of them all. Your Nicolas is handsome, though. To my eye it's a bit sharper and leaner, maybe has more vigour, than Centaur.

About Seria Sans - I look at it and see great concentration and care being taken in drawing those verticals. I think, though, that it's another sans which is perfectly well scaled on its own, but seems all of a sudden over-large, even gross, in company with Centaur, like Shrek with Fiona before she morphed. A quest is in order.

PJ, are you taking relative size into account?
The request is for a body text sans to accompany Centaur at display size.

As soon as Centaur acquires any size, its details start to make it look chiseled and horsey, as if drawn with a big old pen on rough paper. That's not stately.

Therefore, an angular, humanist sans such as Seria Sans or Fedra, at a smaller size, will harmonize with it.

>What sans-serif font would you [...] recommend for the body, if I were to use Centaur Regular for the headings?

I think, and this goes back to some of my earliest posts on the topic of font family compatibility, if you you just give us one point to think of, like you're using Centaur heads, 360 degrees or a veritable universe of body types are possible.

If, on the other hand, you give us two points, like you're using Centaur heads for a medical journal... you know what can be drawn through two points.

Nick, I had sort of forgotten that little point about titling vs text. In that case, I would go with Legacy sans, which looks fine when not chockablock with Centaur in the text. My apologies to imightberebecca for being inattentive.

Also, in speaking of Centaur's form, I had in mind the original, which I think is much better represented in digital form, however imperfectly, by Bitstream's Venetian 301, rather than the clumsy Monotype version, which does deserve your aspersions.

A rough look: