On 11 May 2010, Riveros signed for Sunderland of the English Premier League on a three-year-deal, saying "The league is very competitive and I look forward to being very successful with Sunderland. The Premier League is the best league in the world and Sunderland are a very big club with many passionate supporters. I look forward to meeting them."
He made his Premier League debut on 14 August 2010 as a 63rd-minute substitute for Steed Malbranque in a 2–2 draw against Birmingham City in the opening game of the season. However, Riveros quickly fell out of favour and played just 14 league games for, the club, scoring his only goal on the final day of the season in a 3–0 win over West Ham United.
Riveros during a friendly match against Australia in October 2010
Riveros played in Paraguay's first two matches at the 2006 World Cup and played efficiently on the left wing. He picked up his first international goal for Paraguay in a 3–2 defeat to Chile. He also played for Paraguay in the Copa América 2007.
On 4 May 2010, he was named in Paraguay's preliminary 30-man squad for the 2010 FIFA World Cup, and also made the 23-man penultimate selection alongside club team-mate da Silva.
On 20 June 2010 at the World Cup, Riveros scored a second goal in a 2–0 win over Slovakia, which was set up by former Sunderland defender Paulo Da Silva. Riveros scored a penalty in Paraguay's shoot-out win against Japan in the Round of 16 stage, after the match finished goalless after extra time.