Based on my limited knowledge of icelandic, I will make some more corrections and guesses
Lítla sřta Elinborg viđ sóljugulum hári - Little sweet Elinborg with hair yellow as the sun
hon syngur og hon dansar frítt - she sings and dances freely
og frřist nú um váriđ. - and enjoys the spring
Hon spćlir sćr viđ blómurnar - she plays among the flowers
hon elskar vakrar litir - she loves beautiful colours
sum ein fřgur sóljudrotning - like a fair queen of the sun
í grasinum hon situr. - in the grass she sits
Elisabet Maria viđ vřkrum, bláum eygum - Elisabet Maria with beautiful blue eyes
hon málar vakrar málningar - she paints beautiful paintings
viđ gulum og viđ reyđum. - in yellow and red
Hon málar allar litirnar, - she paints all the colours
sum dagurin man eiga, - that the day can have
sum ein fřgur stjřrnusól - like a fair sunstar
Elisabet Maria.
Brátt so verđur friđarligt - Soon it will be calm
og fuglaveingir hvíla - and the birds rest their wings
sólin bjarta svevur nú, - the bright sun goes to sleep
og mánin fer at skína. - and lets the moon shine
Tá fara tćr til pápa sín - Then they go to their father
sum sřgur veit at siga - who tells them stories
og nú svevur lítla Elinborg - And now little Elinborg is sleeping
og Elisabet Maria. - along with Elisabet Maria
If you have listened to the song on youtube
http://www.youtube.com/watch?v=rsxipQCZCmI
you might want to know what she says before she starts singing.
She speaks in icelandic:
At home on the faroe islands, I have two very sweet little sisters, who are called Elinborg and Elisabet Maria.
And one day about two years ago I was on an airplane on my way to Norway and I missed my little sisters very much and... well, I wrote a song on the plane that is called Elisabet og Elinborg.