We will be visiting Croatia and probably will pick private accomadations to stay in. I'm assuming most privately own places do not take credit cards. So I am wondering the best way to send money for a deposit would be. Also do most of these places just take cash?

Many do take credit cards (I'm a vacation rental owner in Italy and do)...if not, ask them to accept PayPal - it's free for them to set up...and only 3-7% fee to take a cc payment(you could offer to pay...cheaper than a wire transfer!)
-Nicole

Many of the sobes in Croatia only accept cash as payment and we found they didn't require a deposit. However, except for Dubrovnik, we didn't book anything ahead of time. There were many options for places to stay.

Enjoy! It is one of my favorite countries!

Last month we stayed in sobes in 3 different places in Croatia: Trogir, Hvar and Dubrovnik.

The owners of the first two didn't require any deposit so we paid them fully in cash upon arrival.
The owners of the sobe in Dubrovnik asked for the 20% deposit so we got a free Travellers Check in our local AAA office and sent it to them via mail.
Keep in mind that a lot of owners accept both EUR and USD. Also, you can pay in Kunas.

perfectstranger, did you by chance stay at apartment Bakica in Trogir? I ask because I stayed there a few years ago and have such fond memories of the place and the owner. Ah...

In Trogir, we stayed at Marija apartments. www.trogironline.com/marija
It's conviniently located and inexpensive place with nice owners.

Thanks for your replies. I ended up sending a cheque in euros for a deposit. My bank didn't charge me as I'm allowed 12 over the course of a year. We will be landing in Split and need to spend a night there. Any recommentions of a good place to stay?