What technology would be required to detect a coconut-sized sphere in Earth orbit, at the average altitude of communications satellites?
In general, there are two ways to detect objects: Active detection (Radar) and passive detection (optical systems, i.e. telescopes).
Active systems are used for objects close to earth, as the radar systems need to send out their own signal which then gets reflected by the objects. Passive systems are used for objects that are further away, they use the reflection from sunlight (not necessarily visible light, though).
There are also very different types of "communications satellites". The StarLink system is in close orbit (LEO), most western countries utilize satellites in GEO for satellite TV, Russians have to rely on satellites in the Molniya-Orbit, which is highly elliptical and can be in LEO or further away than GEO.
As for radars, which are best for LEO, the size threshold is about 0.5cm-2cm, depending on the radar system.
Optical systems are quite different regarding the detected size, their threshold generally ranges from 15cm ("might detect coconut") to 1m ("won't detect coconut"). These systems rarely watch for random objects in orbit.
Some radar systems keep scanning different regions of the sky, so they have the best odds to find something in lower orbits. An example that could randomly find such an object would be the German FGAN TIRA (potentially aided by the Effelsberg receiver antenna), which could detect your metallic coconut up to a height of 1500km, or the US' Haystack LRIR (potentially aided by HAX). Both do Beam Park experiments.
And just for completeness, there are also optical systems for LEO detection, for example liquid mirror telescopes, but they are mostly being used for statistical analysis.
Note that some of my information might be outdated. It comes from a lecture about space debris, that was a few years back.
Edit, for readability:
Phased Array Warning System (PAWS) - 1980
COBRA DANE - 1977
Eglin radar - 1961
Fylingdales SSN Radar - 1963
Globus II SSN Radar - Before 1998?
FGAN TIRA - 1970
„Monge“ Tracking Ship - 1992
Haystack LRIR/HAX - 1960
Effelsberg receiver antenna - 1971
GRAVES Electronic Fence - 2005