Currently regular services and events are appearing in the order in which they were created.
To order them differently you would need to unpublish the services and events (to find out how to unpublish a service or event click here) and then recreate them again (not just republish them) in the order you wish them to appear.
However, you can choose which Service or Event appears on your church's AChurchNearYou homepage, click here to find out how.
Feedback on current functionality, and requests for new functionality from the AChurchNearYou editors, and from the public, is what drives forward AChurchNearYou feature addition and amendments work.
You can make suggestions direct to the AChurchNearYou project team via this form: https://airtable.com/shrESPQFNe2kaGQQr
You might like to check that it's not something already planned, here's the roadmap for AChurchNearYou where you can find out what's already in the pipeline: https://trello.com/b/L1AxYbvj/a-church-near-you-development