Four collisions have happened on Old Park Estate, resulting in eight casualties and one fatality between May 2012 and 2017.
The new speed limit, dropping from 30mph, will be in force around Old Park Primary School, where parents have previously called for traffic calming measures.
Traffic was monitored outside Old Park Primary School last year after a petition signed by 200 parents and staff was handed in to the council.
Monitoring strips were placed across the road outside the school by the council following complaints by residents about speeding cars, parking taking place on zig-zag lines and people parking across driveways.
It is hoped that the new speed limit, costing £10,000 to enforce, will also prevent cars approaching junctions and crossing areas at speed and provide safer access to shops.
Ward councillor Elaine Costigan, said: "The residents there saw that there was a problem and started to act on it about 16 to 18 months ago.
"They put a petition in to the council and thankfully the council have listened.
"There's been a few accidents on that road, there was quite a few one after another last year.
"I think it's good news and it'll slow people down - it's good news for the families too that walk to the school.
"Police have been in force around the area for quite a while and have been putting notes on cars because of they way they're parked."
She added: "We've done a lot of things about safer parking and we're working hard as ward councillors to listen to our residents.
"I think the new speed limit could be put in place from August."
A resident on Lime Road objected the proposal and said it 'does not meet the needs of the area' but the council have decided to go ahead with the scheme.
Existing signs on the road will be reused and relocated where possible.