Will certain trainers only battle you at a certain time of day?

Question

Ok so I decided to restart Platinum and I noticed none of the Joggers will battle me same with the Police Officers. Will they only battle me in the morning and night? Also are there more trainers like that?

Answer 1

The times that the joggers (4:00 a.m. to 10:00 a.m.) and police officers (8:00 p.m. to 4:00 a.m.) coincides with the availability of certain Pokemon, such as Hoothoot at night (8:00 p.m. to 4:00 a.m.).

So as you can (hopefully) see, joggers and police officers only battle in those times listed above.

Joggers - 4:00 AM - 10:00 AM
Officers - 8:00 PM - 4:00 AM

Source

There are no other timed battles like that, but there are battles that you can have with trainers in different places during different days of the week.
Here is a Link to those trainers and locations.