Many Nigerian shops deliver locally themselves.
LOCAL PICKUP
Add Local pickup to a zone. The customer collects, and no delivery is charged.
Put your address and opening hours in the method description, and repeat them in the order confirmation email.
LOCAL DELIVERY
Either a flat rate on a zone covering your city, or the Local pickup method renamed with a cost, depending on how precisely you need to define the area.
For a tighter area, restrict the zone by postcode where practical.
SETTING EXPECTATIONS
Say when you deliver: same day, next day, or specific days. Vague delivery promises generate enquiries.
Collect a phone number at checkout, which is essential for local delivery and is a required field worth keeping.
USING A COURIER OR DISPATCH RIDER
Charge what it actually costs you, or build an average into your prices. Charging less than the rider costs erodes your margin on every order.
Record the dispatch reference in an order note so you can trace a delivery when asked.