Well, if you want to play exactly like the artist that is performing the song you want to play, then all you can do is listen to it closely.
However, I found it liberating to think of my playing as "playing my version of the song". Because then you can start with an easy pattern that suits the rhythmic pattern of the song (for example D DU UD for any song in 4/4).
After that, you come up with more exotic patterns that match the songs style.
The more patterns you pick up and can play naturally without thinking too much, the easier you will be able to match the artist that plays your song.
Look at Tequilla sunrise by the eagles, it has three quick 16th strums in the second beat of each bar when you listen to the eagles, but you can easily play it in your basic D DU UD.
If you you really can't come up with somethng to play for your song, or if your patterns start to annoy you, make a search on youtube for "acoustic cover", it always helps to see others play.
There's a good book by Tom Kolb that covers rhythm guitar for Folk, Blues, Ballads, Rock, Funk, Latin, etc...
Good place to ppick stuff up.