I too make up heaps of silly songs like rock ballards and change the words - its funny and when I laugh he giggles. I think you'll find once your baby gets a bit older that it will be easier - enjoy that sleepy newborn stage while it lasts
I use the play gym and the bouncer too and I am lucky the older two help out also (no use for a firstborn though).
A sling could be worth trying if you feel comfortable with that - I love it has you can have the baby close to you, but not feel as if you have to entertain them constantly - some babies really do like observing as well.