Ashtami continues till 1.44 PM on 31.03.2012. During the sunrise on 01.04.2012, the extant Tithi would be Navami. This would be Chaitra Navami. Now, keeping besides the fact that Sun should be exalted, you may keep your fast during the afternoon of Ashtami (31.03.12) and celebrate Sri Rama Navami on 01.04.2012.
According to our calender, the day is from sunrise to sunrise. The extant of Navami seem to be more on 31.03.2012, going by this.
As per Sri Rama Jhataka, Punarvasu, 4th pada is the asterism.
Take your pick.