We have no dryer, and are now cloth diapering our second child. From late April to early October I can line dry outside most of the time, but during the winter or when it rains I have to dry inside. To speed up drying time, I sometimes have a fan or two blowing on the diapers. We use prefolds, MEOS fitteds and AIOs; all usually dry overnight.
We also EC - with EC, you actually sometimes use more diapers at the very beginning. 24 diapers is the absolute minimum I would have, but we actually have a lot more than that. My daughter used 10-12 a day when we first started EC with her (at 9 days old; before EC, she was using 20+ per day). By 3 months she was averaging about 6 diapers a day, and now at 7 months she usually wets 4 diapers a day on average. But you can't really predict how EC will work out; my daughter has had days in which she never wet a diaper at all, and days when we were both off and she ended up wetting 10. To be on the safe side, I would recommend 36 diapers. If you have infant prefolds, you can continue to use them trifolded in covers well beyond the suggested 15-pound weight limit.