The work, originally due to start next month, is now planned to begin in September subject to a procurement process.
£16.2m has been allocated to Translink for the railway upgrade.
Last year, Translink said an hourly service on the route was a "priority".
The second stage of the upgrade involves major re-signalling between Derry and Coleraine and the introduction of a passing loop.

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Goals from Liam Polworth and Ross Draper in the space of five minutes put Caley 2-0 ahead at half-time.
A fabulous Miles Storey volley early in the second half sealed a first win in eight games and lifted Thistle to within four points of County in sixth.
County, who were due to parade the League Cup around Dingwall afterwards, spurned a handful of chances.
It was a horrible end to a fabulous week for the hosts, who had recovered from their Hampden heroics to salvage a point at St Johnstone on Wednesday.
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But this proved a match too far after a hectic recent schedule in front of a crowd of just under 6,000.
Alex Schalk, who scored the winner against Hibs at Hampden,  nearly gave Ross the perfect start, but his diving header from Richard Foster's cross was well saved by Owain Fon Williams.
Andrew Davies, who directed a header wide, Jackson Irvine - flicking the ball past Fon Williams but clipping the outside of the post - and Liam Boyce with a header all missed further chances for County.
Storey and Carl Tremarco, with a thunderous volley that cracked off the bar, might have scored for Caley before they broke the deadlock in the 32nd minute.
Marcus Fraser lost possession with County lacking numbers at the back and Storey broke away, found Polworth on the edge of the box and he confidently picked his spot across Woods.
They swiftly doubled their lead when Draper capitalised on space in the area and coolly slotted past the onrushing Woods.
Thistle have struggled for goals of late, but three minutes after the resumption, Storey fired a stunning dipping volley past Woods from the edge of the area to send the visiting fans wild.
Caley were then able to try and pick off their hosts and Josh Meekings came close to connecting at the back post.
Polworth also clipped the bar from distance as a well-executed tactical plan brought a comfortable win.
Work on a second major upgrade to the Londonderry-to-Coleraine railway line has been delayed by four months.
[NEXT_CONCEPT]
A clinical Inverness Caley Thistle spoiled Ross County's celebrations with a fifth straight derby win at Dingwall.