On Saturday they won by five wickets at Clifton Village and then saw off Leicester side Newton Linford at home by four wickets.
At Clifton, Cuckney won the toss and asked the home side to bat before bowling them out for 159 in 38.5 overs.
Only Kiel Van Vollenhoven (48) and Alistair Walters (36) offered real resistance with a fifth wicket stand of 66, Clifton only adding another seven runs as the tail end was quickly mopped up.
Drew Owen took 5-17 from his superb 5.5 overs and Kiwi debutant Andrew Hazeldine claimed 3-32.
Cuckney then reached 163-5 in 35.2 overs. They lost two wickets on 29 but Tom Ullyott, with 52 not out, and Josh Porter, also with 52 not out, steered them home.
“We had a little wobble on the chase and we were 80-5, but we ended up knocking them off – it was a professional performance in the end and Drew bowled brilliantly in the middle of it as they tried to up the rate,” said assistant captain Richard Bostock.
On Sunday it was Cuckney's opening batsman Nick Keast who stole the show against Newton Linford.
Linford were bowled out for 183, with Keast then in magnificent form with 114 not out as they made 185-6 in 37.5 overs.
“It was a brilliant knock by Nick,” said Bostock. We probably let them get 20 or 30 too many. We knew it was a bit of a middling score, but with wickets falling around him Nick played a level-headed innings and saw it through to the end.”
On Saturday Cuckney are away at Attenborough who, after winning their opener, were beaten by Papplewick & Linby on Saturday.
Bostock said: “They are an established Premier League team and have batters and bowlers that can hurt teams, but it's our first home league game and we want to put in a real polished performance.”
In the opening weekend of the newly-formed NPL Division Two, relegated Mansfield Hosiery Mills got off to a winning start after a five wicket victory at neighbours Thoresby Colliery.
Thoresby chose to bat and made 234-8, Ximus Du Plooy with 53 and John Skinner with 42, Danny Tyson adding 29 not out.
Daniel Harris took 3-35 for the Millers.
In reply, Mills made 236-5 thanks largely to a magnificent unbeaten 124 from opener Kamal Manek, backed by Stephen Gooding’s 35 and 24 from Adam Dobb.
Welbeck went down by six wickets at Cavaliers & Carrington seconds.
Richard Stroh hit 60 and Urie Hill 36 but had little support elsewhere as Welbeck were all out for 159, Saif Ali (3-37), Muhammed Yasar (3-7) and Prakhar Singh (3-40) all among the wickets. Cavaliers sailed home in 36.3 overs with 55 for Saqlain Bazmi and 46 for Harrison Tagg.
Clipstone were asked to bat and were all out for 148, David Willcock with 33 and Andy Norwood 31. But they then bowled out Collingham and District for 120 to win it, Ian Woodall claiming 3-16 and Chris Fletcher 3-24.