There is never a good time to announce any iPhone competitor.
* A week before any new iPhone is announced:
Your brand new smartphone only has a week of media coverage before the iPhone flood. And even then, the media has one eye on iPhone rumors, mockups, component spy shots, and record sales forecasts.
* A week after any new iPhone is announced:
Too late. The media is busy analyzing the new iPhone's hardware, software, and content management features. (Because yes, content management is just as important as hardware / OS / apps, in case anyone hasn't noticed already.) There will be endless stories all about the new iPhone. And any story that mentions your brand new competing smartphone will compare it to iPhones new and old. Sorry. That's a fact of life now. iPhone is the benchmark by which all smartphones are measured. And measure they will.
So let's move your smartphone launch as far away as possible from the iPhone launch. 6 months away. That's March 2013. Oops. That will be just about the time that the "new iPad (4th gen)" will be hitting the stores. There will already have been a month of media attention on next-gen iPad rumors, mockups, premature case manufacturing runs, component supplier leaks, iOS feature leaks, and the lead-up to the actual new iPad announcement. Apple will be in the spotlight again. So maybe March isn't the best month to intro an iPhone competitor.
So how about 3 months before or after the iPhone announcement? Split the difference. How about 3 months after the iPhone announcement? Is that a good time? Nope. Announcing a smartphone in mid-December is too late to ride the holiday sales wave. OK, so how about 3 months before the iPhone announcement? Negative. That's June. Summer is the season of Apple's yearly WWDC event in San Francisco. When the next-gen iOS release will be announced and made available to developers. Your smartphone's OS will be up against next-gen iOS, with the inevitable rumors of next-gen iPhone hardware features. Oh, and yes, the next-gen iOS' content management infrastructure will be front and center too.
Speaking of which, how's your iCloud competitor going? Because if you don't have an extremely strong answer to iCloud, you might as well get out of the smartphone business and go back to selling Netbooks.