Is there a standard format or placement for photo credits?

Such standards are usually up to the discretion of the publisher / reprinter, possibly subject to certain limitations, restrictions, or specification by the licensor. This allows for some creativity on the part of the person/organization licensing the photo to create a unified style for their publication.

• Associated Press: immediately following the caption, in parentheses: "(AP Photo/Alan Smithee)". (No link for the the AP Stylebook, it is not available digitally gratis).
• The Association of Art Editors has their own style guide which covers a wide range of types of publications, display, or other reproduction of images. Each type of publication has subtle different suggested ways to credit images.
• Reuters' Handbook of Journalism even details how the photographer should compose, crop, edit, and caption their own photos.
• BuzzFeed's styleguide dictates that credits should read: "Alan Smithee / Agency", and that caption and credits should not be italicized or set in smaller type face.
• Wikipedia's Styleguide dictates that, at a minimum, the artist's name is given, and the title of the work (if available) is set in italics.

The list goes on. Any professional publication or publishing group will have a style guide spelling out these details (and many, many more) (and if they don't, I question how professional they are).