I confess that I gave up on Google Custom Search for my (small scale) web sites. I found that Google just wasn't spidering my site regularly or deeply enough to be effective.
I have turned to
Atomz for site searches.
Two caveats:
1. I have not tried it on a Nabble forum, as I find that Nabble's internal forum search works very well for that.
2. Where I have an embedded forum within a site, I have not yet tried to add a further domain to my Atomz settings to make it search both the main site and embedded forum.
Volunteer Helper - but recommending that users move off the platform!
Once the admin for GregHelp now deleted.