You can add Facebook Page badge in Blogger via Facebook iFrame code if you don't get favorable gadget to add.
Please share your feedback to below comment box, like the Facebook page and tweet (all given side panel).
In Facebook Side
- Go > https://developers.facebook.com/docs/plugins/page-plugin. (You can also can reach the same location visiting number of pages. Go https://www.facebook.com/badges, click "Get Social Plugins", click "Page Plugin".)
- Provide Page address, expected width (I have provided 250), height, check/uncheck required option as per requirement.
- Click "Get Code". Select "IFrame", and copy the code.
|Picture: Facebook Page Plugin Area in Facebook|
|Picture: Java/HTML Code Box in Blogger|
In Blogger Side
- Login to your blogger account, click "Layout".
- Click "+ Add a Gadget"
- A new window will appear. provide a heading, example: "ABCD Facebook Page".
- Now, paste the IFrame code which has been copied from Facebook.
- Click Save, and see preview.
|Picture: Sample outcome in right pane of your blogger page|