Hi! I know this is an old post (and hopefully you've found what you are looking for by now!) but just in case, Auckland Christian Assembly sounds perfect for what you are looking for!
They have a 10am Morning service - the usual format is: Worship (songs), testimony, talk, prayer for healing, song & communion, followed by 'voice gifts' (tongues, interpretation and prophesy), then a song to close, notices etc
All baptisms are by full immersion, the church is strong on 'receiving the Holy Spirit', the sign of which is speaking in Tongues. (Acts 2)
Drinking, smoking, etc are not accepted
They also have a smaller evening service at 7pm, this is seen as the 'youth' service, the worship is a little bit louder, the songs are more modern and gutsy. The talk/word is usually given by a member of the assembly (not a pastor) - generally a younger person 18 - 35 yrs. Amazing to hear what different people have to offer! There is then a time of prayer, which sometimes leads into the spiritual gifts again.
ACA is a great church for all ages! Hope this helps!
You can find it at: 26 Albany Highway, Glenfield
P.S. Our Christmas Service is on Sunday the 22 December, there will be items and performances by many talented people, followed by a yummy traditional Christmas lunch - free! All welcome!