SINGAPORE, Aug 29 (Reuters) - Asian equity markets struggled for direction on Tuesday as the bounce from Beijing's efforts to support stocks ebbed, while bonds rallied and the dollar dipped ahead of U.S. labour and manufacturing data due later in the week.

Amid growing expectations those data points could come in soft, U.S. Treasuries extended overnight gains, driving two-year yields down 6.5 basis points (bps) to 4.9855% and 10-year yields down three bps to 4.1843%.

That put some gentle pressure on the dollar, which has slipped below its 200-day moving average to $1.0833 per euro and was slightly lower on other majors in early trade.

The yen remained an outlier and within a whisker of Monday's 10-month low, which has traders on edge about the risk of intervention. The yen last bought 146.34 per dollar.

MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.4% as did Japan's Nikkei.

"After opening strongly Hong Kong and China gave up most of their gains yesterday and commodities remain unloved," said Damian Rooney, a dealer at Argonaut Securities in Perth, since measures cutting stock-trading duties do little for the economy.

Over the weekend, China announced a halving in stock-trading stamp duties and had on Friday approved some guidelines for affordable housing.

Hong Kong's Hang Seng closed less than 1% higher on Monday and was 1% firmer in early trade on Tuesday. Mainland blue chips were flat and the month is set to notch a record for foreign outflows from the mainland stockmarket.

Even on Monday, as markets bounced, foreign investors offloaded a net $1.1 billion in Chinese stocks and have been net sellers in 15 out of 16 previous sessions - keeping downward pressure on the yuan.

The yuan steadied at 7.2876 per dollar.

Highlighting the focus on property sector fears, shares in indebted developer China Evergrande, which dropped nearly 80% upon their return from suspension on Monday, were down a further 6% on Tuesday.

"The underlying problem appears to be the adjustment in the property sector and its spillover to the rest of the economy," Bank of Japan Governor Kazuo Ueda said at the Jackson Hole symposium.

Beneath the headline moves, individual shares offered some brighter spots.

Overnight shares in conglomerate 3M jumped 5% after the company's promise to pay $6 billion to settle a lawsuit over its earplugs was smaller than some analyst estimates of liabilities around $10 billion. Goldman Sachs shares rose after it struck a deal to sell part of its wealth business.

On Tuesday in New Zealand shares in Tourism Holdings , the world's largest campervan rental company, surged 13% after the company reported a record underlying profit.

In currency markets, sterling and the Australian and New Zealand dollars made small gains, with the pound last up 0.2% to $1.2625 and the Aussie up by the same margin to $0.6442.

In commodities, Brent crude futures slipped 0.2% to $84.27 a barrel. On Tuesday, U.S. job openings figures are due, ahead of Friday's broader labour market data and the ISM manufacturing survey.

"There's anticipation of a bit of a slowing in the labour market and cooling of the inflationary pulse," said Ryan Felsman, senior economist at the Commonwealth Bank of Australia in Sydney.

(Additional reporting by Jason Xue in Shanghai. Editing by Sam Holmes)