* New private homes in tier-1 cities -0.2 pct m/m vs -0.3 pct in Aug : BEIJING (Reuters) - China’s new home prices registered a second straight month of weak growth in September, with prices in the biggest markets slipping and gains in smaller cities slowing as government measures to cool a long property boom took hold. China’s housing market has been on a near two-year tear, giving the economy a major boost but stirring fears of a property bubble even as authorities work to contain risks from a rapid build-up in debt.