Just keep trying to do it and it will come. Maybe start with a song that you can either sing with little thought that isn't challenging or that you can play on the guitar with little thought that isn't challenging. Play a very simplified rhythm on the guitar if you need to just to get the feel down.

I sing backup in my duo and at first it felt impossible. As soon as I would start singing my guitar playing would fall apart. Eventually it started to come together and it feels more natural. For me it took 3 or 4 months to get where I could sing/play more complicated things together. I still need to work on my singing by itself :).

Now being the backup singer, I have the luxury of dropping out if I need to...and that was what I did on occasion. If my guitar playing started to fall apart, I shut my mouth :).