Euro zone bonds give cautious welcome to U.S.-China trade progress

* German yields little moved in quiet session

* U.S.-China trade negotiators appear to make progress

* Italian yields fall further from 2% level

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr

LONDON, May 8 (Reuters) - Euro zone government bond yields were little moved on Friday as investors gave a cautious welcome to U.S. and Chinese trade representatives agreeing to strengthen cooperation, while the more positive mood helped Italian borrowing costs to fall.

Government bond markets have had a volatile week after a German constitutional court ruling threatened to jeopardise one of the European Central Bank's bond buying programmes unless it can show the scheme is proportional.

That has worried investors about the future of the ECB's emergency purchase scheme and sparked a sell-off in Italian debt, which is dependent on ECB purchases to keep borrowing costs down.

Hefty issuance of new government bonds this week to fund coronavirus stimulus plans has also pushed yields higher.

But on Friday the market was calm, as investors digested news that U.S. and Chinese trade representatives discussed their Phase 1 trade deal on Friday, with China saying they agreed to improve the atmosphere.

Jan von Gerich, a fixed income analyst at Nordea, said he believed the market was overly optimistic about the deal.

"When it comes to (U.S. President Donald) Trump, everything is uncertain ... But it will be very difficult for China to hold in this environment to those commitments in the trade agreement," he said, referring to the economic hit China faces from the fight against the coronavirus outbreak.

The German 10-year yield was unchanged on the day at -0.548% . Other core euro zone yields were also unmoved.

On the economic data front, the big news of the day will be U.S. payrolls figures which are expected to show the American economy has lost the most jobs since the Great Depression.

But analysts said backward-looking economic data had generally been ignored by bond markets, with much more interest in the speed at which lockdowns are lifted and evidence of when an economic recovery would take hold.

"It seems at least in the euro zone that economic data is not the main driver and there's more interest on the political front," von Gerich at Nordea said.

Italian yields dropped in early trade. The 10-year yield was down 3 basis points at 1.873%, pulling it further away from the 2% level it hit earlier this week. Some economists say borrowing costs above 2% start to throw Italy's debt sustainability into danger.

Shorter-dated Italian debt yields also dropped, with the five-year yield at 1.412%, 5 basis points lower on the day. (Reporting by Tommy Reggiori Wilkes; Editing by Mark Potter)