The EXIF specification for JPEG metadata says:

The date and time of image creation. In this standard it is the date and time the file was changed. The format is "YYYY:MM:DD HH:MM:SS" with time shown in 24-hour format, and the date and time separated by one blank character [20.H]. When the date and time are unknown, all the character spaces except colons (":") may be filled with blank characters, or else the Interoperability field may be filled with blank characters. The character string length is 20 bytes including NULL for termination. When the field is left blank, it is treated as unknown.

Which allows for entirely unknown dates, but doesn't have a standard for less-precise dates. You could fill unknown portions with spaces, but I'm not sure which software will let you do that, and more importantly, which software will react badly to reading that, since the standard does not explicitly give that as an option.

I think you have two basic choices:

• Option 1: Guess. Based on the subject matter, put in your best guesses for the date and time.
• Option 2: Chose a clearly-arbitrary value like midnight on January 1st of the appropriate year — YYYY:01:01 00:00:00. When someone looks later, they probably won't think that the pictures were all from some wild New Year party.

The latter can be combined into the former. When I know the day but not the time, I usually set the time to noon: 12:00:00, because this avoids (a large degree of) time-zone ambiguity. (Another unfortunate lack in the EXIF standard.)