Hi Rafiwa, there are a number of primary schools that you could try. One of the best (well, prob the best) in SEELB area is Harmony Hill Primary School, Harmony Hill, Lisburn they also have a pre-school - which is fantastic. It's a great Primary School and the kids do well.
I know that a few of the mums would use Barbour Nursery if their Primary School doesn't have a nursery. It takes children from (I think) 9.00am until 2.00pm.