Goulding is a former St. Edmund Arrowsmith pupil. he played for the junior amateur club Wigan St. Patrick's in Ince, Wigan. He was part of Wigan's scholarship scheme and played in Wigan's Academy U18s in 2004 and U21s in 2005.
Goulding signed a two-year full-time contract with Wigan in July 2005, and was drafted into the first team squad for the first time in August 2005 and shortly after made his début against Widnes.
He scored his first try for Wigan in the 48-22 loss to Leeds on 9 June 2006.
On 6 April 2009, Warrington centre Martin Gleeson transferred to Wigan in a deal rumoured to involve Goulding, since he had only been played twice in Wigan's first ten Super League matches. However, this rumour was rejected when Goulding was released on loan to Salford on 14 April.
Darrell made his Reds' début in Perpignan, France in the defeat at the hands of Catalans Dragons. He made his home début a week later at the Willows, scoring two tries - including a 70-metre interception score against Hull. He added a third for the Salford club in his next Super League game - the away victory at Huddersfield.
After returning to Wigan in 2010, Goulding had a breakthrough year, filling in for the injured Amos Roberts for the majority of games. He finished the year with 20 appearances and 25 tries, joint second highest scorer in 2010.
His 2011 season started against St. Helens at the season-opening Magic Weekend event. After opening his try tally at Bradford in Round 2, he scored again at Salford in Round 4 and featured in the 2011 World Club Challenge team that lost to St George Illawarra Dragons. Goulding made five further consecutive appearances, including a try in Round 8 against Leeds, but was dropped after their loss in Round 9 to Catalans Dragons, in which Goulding's error under the high ball had handed Frédéric Vaccari a try. He reappeared for Wigan's Round 13 win against Crusaders RL.
It was Goulding who also scored the try just before half time in Wigan's 2013 Grand Final win over Warrington Wolves. His try brought the score back to 16-6 after the Warriors went 16-2 down and Wigan came back in the second half to win 30-16.
In July 2014, Hull Kingston Rovers announced that Goulding had signed a three-year contract with the club starting from the 2015 season. Just 8 matches into his Hull KR career, however, Goulding was forced to retire from the sport due to a string of concussion injuries. His retirement was formally announced on Monday 1 June 2015.
Darrell was selected for Lancashire U17s, England U15 and U16s while part of the Wigan scholarship system. He was also included in the England U17s squad to take on the touring Australian Institute of Sport in 2005. In September 2010 he was called into the senior England squad for the first time for the 2010 Four Nations series in Australia and New Zealand, although he did not feature in the tournament