* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Recasts lead, adds details) AMSTERDAM, Oct 2 (Reuters) - Italy’s 10-year bond yield fell to a record low on Friday after September data showed euro zone inflation sinking deeper into negative territory and rising coronavirus cases across the continent raised expectations for more stimulus from the European Central Bank by yearend The rush for safety was further exacerbated after U.S. President Donald Trump tested positive for the coronavirus, ramping up uncertainty ahead of November’s presidential election. Euro zone inflation dropped to minus 0.3%, according to the first estimate for September, its lowest level in over four years. The decline into negative territory was deeper than expected, and another reading tracked closely by economists, excluding food, energy, tobacco and alcohol, fell to a record low of 0.2%, stoking concerns of a deflationary spiral. The figure, which was worse than initial forecasts, was largely expected after German and Italian inflation readings missed estimates earlier in the week. A key market gauge of long-term inflation expectations fell to its lowest since mid-July at 1.1339%. “If there is no improvement in the data, Lagarde should announce an expansion of the bond purchase programme before end of the year,” said Nicolas Forest, global head of fixed income at Candriam, referring to ECB President Christine Lagarde. The data comes as divisions between dovish policymakers at the ECB have become more evident, and Lagarde set the scene for a change to the way the bank targets inflation earlier this week. Italian debt outperformed the broader demand for fixed income, pushing the 10-year yield to a record low of 0.735%, according to Tradeweb, which cites the August 2030 benchmark . It was last down 4 basis points on the day at 0.785%. The risk premium Italy pays over 10-year German debt fell to 132 bps, its lowest since Feb. 24. Italian bonds have continued to see support this week despite weak economic data and talk of delays to the European Union’s recovery fund, as investors favour higher-yielding assets. “BTPs narrowed versus Germany regardless through risk on and risk off, which I think is important, because you could argue that there is an asymmetric risk on offer here,” said Richard McGuire, head of rates strategy at Rabobank. He was referring to the likelihood that the ECB will add to its stimulus, of which Italian debt would be a primary beneficiary. Safe-haven German 10-year yields fell as low as -0.551% in early trade just off their lowest in nearly two months, reached earlier this week. They were last down 2 bps at -0.54%. (Reporting by Yoruk Bahceli; editing by Ana Nicolaci da Costa, Mark Potter, Larry King)