If you only have 2 days in the Lisbon, I would strongly suggest you do not plan to go far from the city.
With a child, places like Lisbon Zoo (http://www.zoo.pt)( Site currently being remodelled), the Oceanarium at Parque de Nações ( http://www.oceanario.pt/ ), and the beach at Estoril,(30 minutes by train from Cais de Sodre train station) (http://www.golisbon.com/portugal/cities/estoril.html),would be your best bet.
Finally, a open top city tour is always a great thing for kids.
See: http://goo.gl/rbFqC
All the above are accessible by public transport (Metro/Train)
As regards accommodation it depends on your budget. One of the several IBIS hotels could be a good bet with kids. Alternative, you could have a look at:
Residencial Portuense (http://www.pensaoportuense.com/default.aspx)
and/or
Residencial Florescente. ( http://www.residencialflorescente.com/ )
I have stayed at both and they are welcoming and very central.
