Slide out keyboard is out of the window for any decent spec phones. For now. 4.7" screen phones are considered as tiny.
There are some 4" model, but they aren't worth their money. The Galaxy S4 mini come close, but it's overpriced for the spec it come with.
Asus Zenfone 4, releasing soon, may match what you are looking for. I don't think it's a great phone. Even though it have 4" screen only, it's only 480p and quite large due to the bezel. The Moto G which for being only 5mm wider and longer, have 4.5" 720p screen and quadcore, and running stock Android which undoubtedly will be a much smoother experience.
All of these are in the mid 120mm x 60 mm size, which are still too big compared to a Xperia Mini.
I'll see if I can find anything else, but for what you're asking may have to settle with one of those lowend Samsung Galaxy 3.5" phones or an iPhone 4S.