I see this hasn't been updated in a while so allow me to share the current state of play
As of 4 October 2019...
21 quotas earned in 6 different sports
Sports with quotas earned in alphabetical order:
Athletics
Ciara Mageean (1,500m)
Alex Wright (20k walk)
Brendan Boyce (50k walk)
Others that would get place by virtue of their ranking would be Thomas Barr, Mark English and Phil Healy. Of the highly rated juniors high jumper Sommer Lecky and heptathlete Kate O'Connor have the best chance of making the early step up.
Canoeing - Slalom
boat (men's C1)
Ireland are unlikely to qualify any more boats in canoeing with our best sprint canoeist being Jenny Egan who specialises in longer (non-Olympic) distances
Equestrian
Eventing (team with 3 individuals)
Dressage(team with 3 individuals)
The eventing team won silver at last world champs and individual medalists in last Worlds and Europeans mean they are serious Olympic medal contenders. The first Irish dressage team was a nice surprise. The show jumping team can win medals, but they need the final qualifying spot this weekend to make it after 7th place finishes in the world and euro champs.
Modern Pentathlon
Natalya Coyle
Natalya will be hoping for her third top 10 placing in the Olympics in Tokyo. Arthur Lannigan O'Keefe could medal if everything goes right but he struggled with injuries. He needs to have a great start to 2020 to shoot up the rankings.
Rowing
w1x
w2-
m2x
lm2x
Whoever is with Paul O'Donovan in the lightweight double sculls will be a medal favourite in Tokyo. Paul has won the last two world championships, one with his Rio medal winning brother Gary and the other with newcomer Fintan McCarthy. Sanita Puspure is double world champion and only injury or horrendoes luck will stop her from medaling in Tokyo. The mens double won silver this year and are improving all the time. Ireland will try and qualify a womens 4 next year
Sailing
Laser Radial
Aisling Kelleher won the quota but Rio medalist Annalise Murphy has dropped her 49er FX plans to try and get in the Radial boat for Tokyo. The 49er crew have a good chance of qualifying in December and we might sneak in a Laser quota too next year with most European countries already in.
Swimming
Darragh Greene (100m, 200m breast)
Shane Ryan (100m back)
Irish swimming is one of the only sports that have stricted rules than the IOC for qualifying so neither of thes may actually go. Greene achieved his time at the worlds so has to get close to it at the irish nationals in 2020 to validate it. Everyone else, including Ryan, has to earn the OQT at the irish nationals. Brendan Hyland and Mona Mcsharry look the two most likely to add to the team in individual events but iris swimmimg is aiming to bring a 4x100m medley relay team and is currently OK in the ranks
Likely/possible quotas in these sports
Badminton
Nhat Nguyen is currently in a rankings spot. The mixed doubles of Sam and Chloe Magee are also in a spot, but their quota is far less secured.
Boxing
Traditionally our strongest Olympic sport. Ireland will eb hoping to have at least 8 of the 13 quotas available next year. Our womens team is particularly strong and they'll hope to win 2/3 medals next year.
Cycling
We're very likely to qualify 3 for the mens road race 9with one of them also in the ITT). On the track we should qualify at least 2 women (madison rankings) and maybe one man (omnium).
Diving
Oliver Dingley and Clare Cryan have hopes for next year through the world cup series. Dingley should be OK
Field Hockey
Both mens and womens team face Canada ine 3/4 weeks time in the play offs. The World Cup runner up women are at home and hopefully qualify for their first ever olympics!
Golf
Ireland will qualify 4 for golf next year with McIlroy and Lowry being medal contenders on their day in the mens.
Gymnastics
On this weekend, with luck Emma Slevin and Andrew Steele may qualify for all around (need luck though!). Rhys McClenaghan is a medal contender if he qualifies in pommel!
Judo
We currently have 3 judoka in ranking positions; Ben Fletcher, Megan Fletcher and Nathan Burns
Taekwondo
Jack Wooley is top 8 ranked in the minimum weight and should be OK to amek his first games with average luck.
Triathlon
Russell White and Carolyn Hayes are our best hope of qualifying for Tokyo and both are just inside the quota spots at the moment. Hayes was 6th at the European Championships in May and is a relative newcomer to the sport. She'll easily shoot up the rankings list with performances like that. The ranking period ends in May 2020.
It's unlikely we'll have qualifiers in other sports but maybe the rugby sevens team can surprise us or someone new comes along next year!