Say the count s 1 and, 2 and, 3 and ,4. or

1, 2 and a, 3 e and a, 4 e and a.,1

See I have to sing on the highlighted beats. When I'm playing guitar with these kind of rhythms I don't have any trouble,I guess because I can count out loud plus I have upstrokes and downstrokes to help me.

But how am I supposed to sing in time when melodies are heavily syncopated?
Instead of counting out loud, try counting in your head. Also, try getting someone to clap on the beat and sing on the off-beat, so you can get a feel for it, then try it without the other person.

It is about practise, so if you really want to do it then practise it a lot. Also, listen to lots of music that has this sort of stuff in it or (if possible) a recording of what you're supposed to be singing.

Although i try and stay away from very ambigous statements like this, i think you should try and feel the music. Listen out for which instruments play on the beat and wich on the off-beat, then you can use it like you did the clapping or sing at the same time, respectively.