While it may be somewhat uncommon to use the word contemporary to refer to living people, 'Merkel is a contemporary of Obama' is an acceptable statement.
However, the term does introduce some possibility of ambiguity. For example, the phrase contemporary critics of Shakespeare could be interpreted as referring to critics that were contemporaries of Shakespeare or as modern critics of Shakespeare.
coeval generally refers to very long or remote periods of time. It probably not be suited to refer to individuals.
Coeval refers either to very long periods of time—an era or an eon—or to remote or long ago times: coeval stars, shining for millenia with equal brilliance; coeval with the dawning of civilization.
That page also discusses the nuances of some other similar words such as contemporaneous and coincident.
Also note that the term living contemporaries is usually used in a situation where many of the contemporaries are dead. For example, one might use the phrase, 'living contemporaries of Hemingway' to specifically refer to individuals who are contemporaries of Hemingway, but who are still alive, but it would be very strange to talk about the 'living contemporaries of Obama'.