The expression "agree a time" is correct and usable in written English.
You can use it when you are attempting to arrange a meeting or appointment with someone. For example, "Let's agree a time for our meeting next week."
To agree a time is especially 'exciting' is pointless.
Or you can contact charities such as the British Heart Foundation directly to agree a time and date for collection.
"Therefore, looking forward to a sustained process of dialogue aimed at producing concrete results and in order not to repeat the experience of Istanbul, I would propose that we resume our talks at a mutually convenient date and venue as soon as possible," Ashton concluded, adding that junior officials should meet in the near future to agree a time and venue.
Agree a time you'll be home with your parents, and always make sure you keep to it.
He says both sides have worked hard to agree a time-limited implementation period.
RB had agreed a time and date for the plumber to come to his home.
There was a game of Ulak Tartysh taking place the following day, so we agreed a time and a place and met our fixer the next morning.
Potential interviewees were contacted and asked to participate and if they agreed a time was set either for a face-to-face or telephone interview, dependent on the interviewees' preferences.
All 23 were emailed seven months after the conference, invited to re-confirm their willingness to take part and agree a convenient time to be interviewed.
Potential participants were contacted by the researcher via telephone at least 48 hours after providing initial consent, to agree a suitable time for the interviews.
Buyers and investors alike agree a one-time knock on earnings beats a drag that lasts for years.
