The Wizzrobes can convert a town to their side by building a church near it, making it rebelling after some turns, and then just walking in. That means you can snatch the towns of your allies that way, and that won't put you in bad terms with them. You are the only faction that can convert it's allies from the inside. And it just so happens you start with a diplomat. Also, as you don't have a starting town, you are free to start converting wherever you want in the beginning: as long as their religion is close enough to yours (they must worship, or at least aknowledge the goddesses), you can take their cities.
So here is what I did: turn 1, I tried to ally myself with Hyrule, but they refused (no surprise here). So turn 2, I sent evryone North to the Lanayru Province, put up churchs next to each of their cities, and allied myself with them (they are weak and without any ally in the beginning, so they gladly accepted). Then I waited... And waited... And waited... 15 extremely boring turns. The only thing I did all this time was sending my diplomat on a world trip and allying with everybody I could: first the gorons, then the zoras, then the kokiris, then the gerudo, then the zuna, then the darknuts... Why? Well: who would dare to attack me with all those guys backing me up? Plus, having lots of alliances gives you good reputation. And, most important of all: I can take my allies cities, while they can't take mine...
What happened eventually was that I converted the two Lanayru towns, and the Zunas (being a NPC race) gave me theirs quickly, so in the end I had four regions, a ton of allies everywhere, and I still wasn't at war with anyone. From here I started putting churches in Hylian and Gerudo territories to link my ex-Lanayru cities with my ex-Zuna ones... Then I stopped playing, because peace is boring.