Navigate to APKMirror. Find a version labeled:
Example filename: com.google.android.gms_22.48.18_(040400-338105857)-22481818_minAPI19(armeabi-v7a)(nodpi)_apkmirror.com.apk download google play services apk android 4.4.2
If the regular APK install fails, you can force-install using Android Debug Bridge (ADB) from a PC. This bypasses some package manager restrictions. Navigate to APKMirror
Requirements: PC, USB cable, ADB & Fastboot tools installed. Example filename: com
Steps:
com.google.android.gms_21.48.15_(100400-XXXXXX)-240_API19.apk