Is there an equivalent of "bless you" for coughing?

There is not an equivalent expression.

The all-seeing eye of Wikipedia turns to the subject, and reveals (with multiple citations)

The practice of blessing someone who sneezes, dating as far back as at least AD 77, however is far older than most specific explanations can account for.[9] Some have offered an explanation suggesting that people once held the folk belief that a person's soul could be thrown from their body when they sneezed,[9] that sneezing otherwise opened the body to invasion by the Devil or evil spirits,[10][11] or that sneezing was the body's effort to force out an invading evil presence.[9] In these cases, "God bless you" or "bless you" is used as a sort of shield against evil.

Apparently coughing opens no such window to the soul - merely to the lower respiratory tract.

If my colleague were so seized, I might offer a drink of water, a lozenge, or - in extremis - a call to Emergency Services. Verbally, "Are you OK, pal?" might suffice.

Usually I hear the phrase "all right?" or something similar, if someone's coughing a lot. Informally phrased, with nonverbal cues like a sympathetic smile or expression, gentle tone, or even a bit of humor, it means pretty much what you said - acknowledging the cough (or other obvious, obviously minor problem), offering sympathy.

Although it is generally meant as sympathy, asking like this also leaves an opening for the person being asked to acknowledge any problems or make any requests, if they are actually in distress - a nice bonus, and one reason for choosing to use it in such situations.

If someone is actually concerned, that is generally shown by asking more formally, using a concerned or inquisitive tone - "Are you alright?" or "Are you ok?", asking if they need something or offering it like "Need a glass of water?", or asking further questions. That is usually a more specific question - that is, actually asking after the person, checking in on what they need, if they seem in actual distress.

It's not quite the same thing as "bless you", and certainly not, hm, formally equivalent - I haven't seen it written down or spoken about as a response to coughing, but it does serve the same purpose, and when I've heard it used or used it myself, it has not been misunderstood.