Android Studio keeps refusing to resolve com.android.support:appcompat-v7:29.0.1

It happens because com.android.support:appcompat-v7:29.x.x doesn't exist.

You can check the revision history in the official doc.

You can:

• Use the last 28.0.0 release of the support library
• migrate to androidx

Also check this note:

Note: With the release of Android 9.0 (API level 28) there is a new version of the support library called AndroidX which is part of Jetpack. The AndroidX library contains the existing support library and also includes the latest Jetpack components.

You can continue to use the support library. Historical artifacts (those versioned 27 and earlier, and packaged as android.support.*) will remain available on Google Maven. However, all new library development will occur in the AndroidX library.

We recommend using the AndroidX libraries in all new projects. You should also consider migrating existing projects to AndroidX as well.

Replace implementation 'com.android.support:appcompat-v7:29.0.1' with implementation 'androidx.appcompat:appcompat:1.0.2'

There is no support library for 29 you have to use androidx support library packages for new developments

from the Docs

This is the stable release of Support Library 28.0.0 and is suitable for use in production. This will be the last feature release under the android.support packaging, and developers are encouraged to migrate to AndroidX.