Not all government agencies participate in the Government Internship Program, and I think only the NYC implements it year-round. I know of some who just implement it for summer.
Interested interns can apply directly at our office. It's at 4th Floor Bookman Building #373 Quezon Avenue, Quezon City. Provincial applicants may inquire with our area offices (it's listed in the website, along with the locations and contact numbers).
We usually hire every two months. The end of this batch's term is on 30 June, so this is a good time to send in your applications for the next batch.
Hope this helps.