You can use withContext function to run a code in background thread and return some result:

suspend fun signUpUser(signUpData : SignUpUserRequest): User = withContext(Dispatchers.IO) {    
    val response = retrofitInstance.socialSignUP(signUpData)
    if (response.success) response.data else response.message
}

If you need to run works in parallel then you can use coroutineScope or async coroutine builder functions. However, in your case you don't have more than a request and so it could be sequantial. As mentioned in previous answer you can use withContext. Here is the small explaination from docs:

Calls the specified suspending block with a given coroutine context, suspends until it completes, and returns the result.

suspend fun getUser(signUpData: SignUpUserRequest): User = withContext(Dispatchers.IO) {
    // do your network request logic here and return the result
}

Please note that, when you are working with expression body with functions, always try to annotate return type explicitly.

EDIT

Coroutines use the regular Kotlin syntax for handling exceptions: try/catch or built-in helper functions like runCatching (which uses try/catch internally). Beware of that uncaught exceptions will always be thrown. However, different coroutines builders treat exceptions in different ways. It's always good to read official documentation or other sources (like this).

In the Google codelab "Load and display images from the Internet", there's a nice and very elegant example with MutableLiveData.

Outline:

• You make a ViewModel with LiveData (internal) and MutableLiveData (external)
• Now you can use the data directly in views, fragments or activities

The benefit being that this data is lifecycle-aware, and you can use the returned values with observers.

class OverviewViewModel : ViewModel() {

    enum class MarsApiStatus { LOADING, ERROR, DONE }

    private val _status = MutableLiveData<MarsApiStatus>()
    val status: LiveData<MarsApiStatus> = _status

    private val _photos = MutableLiveData<List<MarsPhoto>>()
    val photos: LiveData<List<MarsPhoto>> = _photos

    /**
     * Call getMarsPhotos() on init so we can display status immediately.
     */
    init {
        getMarsPhotos()
    }

    /**
     * Gets Mars photos information from the Mars API Retrofit service and updates the
     * [MarsPhoto] [List] [LiveData].
     */
    private fun getMarsPhotos() {
        viewModelScope.launch {
            _status.value = MarsApiStatus.LOADING
            Log.d(TAG, "loading")
            try {
                _photos.value = MarsApi.retrofitService.getPhotos()
                _status.value = MarsApiStatus.DONE
                Log.d(TAG, "done")
            } catch (e: Exception) {
                _status.value = MarsApiStatus.ERROR
                _photos.value = listOf()
                Log.d(TAG, "error")
            }
        }
    }
}

You can use the status or photos values by observing them or directly using them in a view like this:

    <androidx.recyclerview.widget.RecyclerView
        android:id="@+id/photos_grid"
        android:layout_width="0dp"
        android:layout_height="0dp"
        app:layoutManager="androidx.recyclerview.widget.GridLayoutManager"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintLeft_toLeftOf="parent"
        app:layout_constraintRight_toRightOf="parent"
        app:layout_constraintTop_toTopOf="parent"
        app:listData="@{viewModel.photos}"
        app:spanCount="2"
        tools:itemCount="16"
        tools:listitem="@layout/grid_view_item" />

...after you've "registered" and wired everything in the f.ex. regarding fragment, like this:

override fun onCreateView(
    inflater: LayoutInflater, container: ViewGroup?,
    savedInstanceState: Bundle?
): View? {

    try {
        val binding = FragmentOverviewBinding.inflate(inflater)
        //val binding = GridViewItemBinding.inflate(inflater)

        // Allows Data Binding to Observe LiveData with the lifecycle of this Fragment
        binding.lifecycleOwner = this

        // Giving the binding access to the OverviewViewModel
        binding.viewModel = viewModel

        binding.photosGrid.adapter = PhotoGridAdapter()

        return binding.root
    } catch (e: Exception) {
        Log.e("OverviewFragment", "${e.localizedMessage}")
    }
    return null
}