Hi,
1. He was only able to do that.
2. He only was able to do that.
I wouldn't say #2 is wrong, but #1 is certainly much more 'normal' and common.
You might also like to think about these.
He was able only to do that.
He was able to only do that.
He was able to do only that.
Only he was able to do that.
Best wishes, Clive