Núñez grew up in the United States, coming with his family on his father's investor visa in the early 1990s and graduating from W. T. White High School in Dallas, Texas. He was drafted by the Dallas Burn sixth overall in the 2004 MLS SuperDraft after one season of college soccer at Southern Methodist University for which he was named the Missouri Valley Conference player of the year.
In his first year with the Burn, Núñez saw very limited action, playing a total of 107 minutes in eight games. However, he came on strong at the end of his second season, earning a starting role and finishing with five league goals and three assists. After losing a starting spot in, he was traded to Chivas USA in August 2007. He was waived at the end of the season.
Núñez was part of the Honduran U-20 team at the 2005 World Youth Championship in the Netherlands. In October 2006, Núñez was called up to the Honduran senior team. He made his debut for the national side on September 9, 2007 coming in as a substitute in a match against Costa Rica. Ramon has had an impressive performance with the Senior Team in September. Ramón Núñez scored two goals for Honduras after the team was losing by one goal to Canada on September 6, 2008 to defeat the squad 2-1. Four days later he would score again for Honduras against Jamaica where the team won 2-0.
He's currently The Player Of The Moment in Honduras.