Dougie Imrie’s outfit will play host to Falkirk on Saturday 9 July, with kick-off at Cappielow 3pm.
The match, taking place on Tuesday 12 July, will be shown live on Premier Sports with kick-off 7.45pm.
After a weekend matchday off, the Bairns will then travel to SPFL newcomers Bonnrigg Rose Athletic on Wednesday 20 July, with kick-off also at 7.45pm.
To round off Group D, fellow League 1 side Clyde will travel to the Falkirk Stadium on Saturday 23 July, with kick-off at 3pm.
McGlynn’s side will start off pre-season with a match against Kilmarnock to celebrate the opening of the Kevin McAllister Stand.
That match will take place on Friday 24 June, with a grand opening taking place on the night with kick-off for that one 7.30pm.
While Stenhousemuir will kick-off with two home ties, the first against Ian McCall’s Partick Thistle on Saturday 9 July at 3pm.
They then face Highland League outfit Fraserburgh on Saturday 16 July at 3pm.
Rounding off Group B is an away trip to Montrose on Tuesday 19 July, with kick-off at 7.45pm followed by a trip on Saturday 23 July to Premiership returnees Kilmarnock.
Kick-off for that one is 3pm and Stephen Swift’s side will hoping to have something to play for going up against the top seeds last.