From Ascension to Pentecost 2019, all Christians are invited to prayer for evangelization as part of the ‘Thy Kingdom Come’ initiative (30 May - 9 June 2019)
Thy Kingdom Come is a global prayer movement, which invites Christians around the world to pray between Ascension and Pentecost for more people to come to know Jesus Christ. What started in 2016 as an invitation from the Archbishops of Canterbury and York to the Church of England has grown into an international and ecumenical call to prayer.
On the website (https://www.thykingdomcome.global/) there is a wealth of resources for parishes, families and individuals as well as a series of testimonies. The website also lists local events (perhaps your parish might care to arrange one as an invitation to the unchurched) and a place for you to pledge your support as part of the novena.
There are also particularly Catholic resources available too: https://www.thykingdomcome.global/search/resources?tags=1&theme_id=13
The Holy Father Pope Francis himself prayed that the Holy Spirit would come to all those who attended during a personal message he gave when visiting the Archbishop of Canterbury. See below: