The defensive duo have been selected for the World Cup qualifiers against Sweden in Gothenburg on 22 March and the game with Austria in Dublin on 26 March.
Wilson has been recalled after the Stoke player recovered from a broken leg, while Everton's Coleman is also included after shrugging off a thigh problem which ruled him out of last month's friendly win over Poland.
Trapattoni said: "Last month's friendly game against Poland was a great opportunity to work with younger players, and I saw a lot of potential from them.
"We played very well during the game, and I intend on building from that performance this month.
"These two games against Sweden and Austria are very important, and we are focused on the task in hand.
"I am confident that these players can work together to produce the results we need. Sweden and Austria are two very strong teams, who have done very well in Group C to date.
"However, I believe that our players have the mentality and attitude necessary to qualify. I am looking forward to assembling the squad on March 17."
Republic of Ireland squad:
Westwood (Sunderland), Forde (Millwall), Randolph (Motherwell)
O'Shea (Sunderland), St Ledger (Leicester), Clark (Aston Villa), Wilson (Stoke), Coleman (Everton), Kelly (Reading), O'Dea (Toronto), O'Brien (West Ham), McShane (Hull), Pearce (Reading), Ward (Wolves)
Whelan (Stoke), McCarthy (Wigan), Green (Leeds), Hendrick (Derby), McGeady (Spartak Moscow), Pilkington (Norwich), McClean (Sunderland), Brady (Hull)
Keane (Los Angeles Galaxy), Long (West Brom), Doyle (Wolves), Sammon (Derby), Walters (Stoke), Cox (Nottingham Forest), Hoolahan (Norwich)