Podfile

# "DoingMyThing" is the app name here, replace it with your own, of course

platform :ios, '10.0'
require_relative '../node_modules/@react-native-community/cli-platform-ios/native_modules'
require_relative '../node_modules/react-native-unimodules/cocoapods.rb'

target 'DoingMyThing' do
  # Pods for DoingMyThing
  pod 'React', :path => '../node_modules/react-native/'
  pod 'React-Core', :path => '../node_modules/react-native/React'
  pod 'React-DevSupport', :path => '../node_modules/react-native/React'
  pod 'React-RCTActionSheet', :path => '../node_modules/react-native/Libraries/ActionSheetIOS'
  pod 'React-RCTAnimation', :path => '../node_modules/react-native/Libraries/NativeAnimation'
  pod 'React-RCTBlob', :path => '../node_modules/react-native/Libraries/Blob'
  pod 'React-RCTImage', :path => '../node_modules/react-native/Libraries/Image'
  pod 'React-RCTLinking', :path => '../node_modules/react-native/Libraries/LinkingIOS'
  pod 'React-RCTNetwork', :path => '../node_modules/react-native/Libraries/Network'
  pod 'React-RCTSettings', :path => '../node_modules/react-native/Libraries/Settings'
  pod 'React-RCTText', :path => '../node_modules/react-native/Libraries/Text'
  pod 'React-RCTVibration', :path => '../node_modules/react-native/Libraries/Vibration'
  pod 'React-RCTWebSocket', :path => '../node_modules/react-native/Libraries/WebSocket'

  pod 'React-cxxreact', :path => '../node_modules/react-native/ReactCommon/cxxreact'
  pod 'React-jsi', :path => '../node_modules/react-native/ReactCommon/jsi'
  pod 'React-jsiexecutor', :path => '../node_modules/react-native/ReactCommon/jsiexecutor'
  pod 'React-jsinspector', :path => '../node_modules/react-native/ReactCommon/jsinspector'
  pod 'yoga', :path => '../node_modules/react-native/ReactCommon/yoga'

  pod 'DoubleConversion', :podspec => '../node_modules/react-native/third-party-podspecs/DoubleConversion.podspec'
  pod 'glog', :podspec => '../node_modules/react-native/third-party-podspecs/glog.podspec'
  pod 'Folly', :podspec => '../node_modules/react-native/third-party-podspecs/Folly.podspec'

  target 'DoingMyThingTests' do
    inherit! :search_paths
    # Pods for testing
  end

  use_native_modules!
  use_unimodules!
end

target 'DoingMyThing-tvOS' do
  # Pods for DoingMyThing-tvOS

  target 'DoingMyThing-tvOSTests' do
    inherit! :search_paths
    # Pods for testing
  end

end

For platform :ios, '9.0' I get this:

[!] CocoaPods could not find compatible versions for pod "UMTaskManagerInterface":
  In Podfile:
    UMTaskManagerInterface (from `../node_modules/unimodules-task-manager-interface/ios`)

Specs satisfying the `UMTaskManagerInterface (from `../node_modules/unimodules-task-manager-interface/ios`)` dependency were found, but they required a higher minimum deployment target.

I had to change it to platform :ios, '10.0'

I had to specify the path for node_modules:

use_unimodules!(modules_paths: ['../node_modules'])