Nature has a natural balance. When we over dam rivers we can reduce the rate the water flows at. The reduced rate of fresh water means the sea water pushes in further inland.
Now what role does the mangrove play? The mangrove prevents the soil on the coast from eroding, it acts as a natural barrier against the sea water and helps keeps the waters inland of it full of fresh water from rivers. As we get rid of mangrove we destroy this too.
So what can be done?
1. We can improve water management upstream. If we build reservoirs to store monsoon and floodwater, especially downstream of dams, we can then release the water back into the river throughout the year and keep the riverflow at a higher rate. This could be done via artificial canals feeding into the river near the delta.
2. Plant more mangroves. There is no easier cheaper way to protect the coast.
3. Create artificial barriers in the sea for the tide to break against. This will reduce the rate of flow of sea water into the delta, meaning more fresh water. This is likely an expensive option I think.