Smallbone and Coleman have not played for their clubs since featuring for the Republic of Ireland last month.
Coleman hobbled off with a leg injury in the 2-0 defeat by England.
Smallbone started in both home losses against England and Greece but a hamstring issue has prevented him from playing for Southampton since then.
Taylor, 26, has been in previous Republic squads but the Ipswich midfielder, who made seven appearances for the Irish Under-21 in 2019 and 2020, is yet to earn a full cap.
The Irish will face Finland in Helsinki on 10 October before taking on Greece in Athens three days later.
Hallgrimsson began his Republic of Ireland reign with last month’s two defeats and will be seeking significant improvement both in terms of performances and results in the Helsinki and Athens contests.
Republic of Ireland squad
Goalkeepers: Caoimhin Kelleher (Liverpool), Mark Travers (AFC Bournemouth), Max O’Leary (Bristol City).
Defenders: Festy Ebosele (Watford, on loan from Udinese), Mark McGuinness (Luton), Dara O’Shea (Ipswich Town), Nathan Collins (Brentford), Andrew Omobamidele (Nottingham Forest), Liam Scales (Celtic), Callum O’Dowda (Cardiff City), Robbie Brady (Preston North End).
Midfielders: Josh Cullen (Burnley), Jayson Molumby (West Bromwich Albion), Jason Knight (Bristol City), Finn Azaz (Middlesbrough), Jack Taylor (Ipswich), Jamie McGrath (Aberdeen).
Forwards: Adam Idah (Celtic), Evan Ferguson (Brighton and Hove Albion), Sammie Szmodics (Ipswich Town), Chiedozie Ogbene (Ipswich Town), Mikey Johnston (West Brom), Troy Parrott (AZ Alkmaar), Kasey McAteer (Leicester City).