I tried using a two-digit date for the year, but I can't complete the batch without using a 4-digit date. I hate to lose the year completely. What can I do?
Yes, and the instructions don't help specifically - and without any Reference Images it's tough to know the exact date. My guess would be 1888-1889 but I guess wait until a moderator can help. The reason for my guess (1888-1889) is the style of the handwriting - but I am not a professional paleographer. I agree with the consensus below - mark it <BLANK> - because if FamilySearch or the record custodian want it to be something else - they probably will do so in pre-publication processes (but I wouldn't hold my breath).
The field instruction for year says:
If only a 2-digit number was recorded, you can sometimes determine the first 2 digits of the 4-digit year from other information, such as the project dates or other contextual information on the image. Sometimes adjacent images give the missing information or additional context.
If you cannot determine the 4-digit year, press Ctrl+B to mark this field blank.
It sounds like they want a 4 digit date or nothing at all. Can you find a year on the reference images? Either going forward or back?
If there isn't any indication on the reference images, then the field is marked blank since there is no indication on the image.