The defender tore a hamstring while on duty for the Republic of Ireland Under-21s last month.
Civelli, 23, had been out for 18 months with a knee injury while Delaney, 29, suffered a blood clot in pre-season.
Full-back Delaney was able to boost his fitness after already playing a full game in the League Cup this season.
Argentine winger Civelli has yet to make a first-team appearance since March 2009.
Reserve-team boss Chris Kiwomya told the club's website: "It was a good workout for the players. Shane did well and got a full game in and Luca will be stronger for his 90 minutes as well."
Source: BBC Sport
Source: BBC Sport