We report results of a direct imaging survey for giant planets around 80 members of the \beta Pic , TW Hya , Tucana-Horologium , AB Dor , and Hercules-Lyra moving groups , observed as part of the Gemini NICI Planet-Finding Campaign . For this sample , we obtained median contrasts of \Delta H =13.9 mag at 1 ” in combined CH _ { 4 } narrowband ADI+SDI mode and median contrasts of \Delta H =15.1 mag at 2 ” in H -band ADI mode . We found numerous ( > 70 ) candidate companions in our survey images . Some of these candidates were rejected as common-proper motion companions using archival data ; we reobserved with NICI all other candidates that lay within 400 AU of the star and were not in dense stellar fields . The vast majority of candidate companions were confirmed as background objects from archival observations and/or dedicated NICI campaign followup . Four co-moving companions of brown dwarf or stellar mass were discovered in this moving group sample : PZ Tel B ( 36 \pm 6 M _ { Jup } , 16.4 \pm 1.0 AU , Biller et al . 2010 ) , CD -35 2722B ( 31 \pm 8 M _ { Jup } , 67 \pm 4 AU , Wahhaj et al . 2011 ) , HD 12894B ( 0.46 \pm 0.08 M _ { \odot } , 15.7 \pm 1.0 AU ) , and BD+07 1919C ( 0.20 \pm 0.03 M _ { \odot } , 12.5 \pm 1.4 AU ) . From a Bayesian analysis of the achieved H band ADI and ASDI contrasts , using power-law models of planet distributions and hot-start evolutionary models , we restrict the frequency of 1–20 M _ { Jup } companions at semi-major axes from 10–150 AU to < 18 % at a 95.4 \% confidence level using DUSTY models and to < 6 % at a 95.4 \% using COND models . Our results strongly constrain the frequency of planets within semi-major axes of 50 AU as well . We restrict the frequency of 1–20 M _ { Jup } companions at semi-major axes from 10–50 AU to < 21 % at a 95.4 \% confidence level using DUSTY models and to < 7 % at a 95.4 \% using COND models . This survey is the deepest search to date for giant planets around young moving group stars .