The administrative centre is Alloa and this is the smallest county of Scotland. Commonly abbreviated to Clacks it is named after an ancient stone which resides in Main Street, Clackmannan.

Clackmannanshire Council

All public car parks in Clackmannanshire are available FREE of charge and are not time restricted. There is no information with regard to motorhomes.

Alloa - King Street cp - Large goods vehicles are allowed to stay overnight. I have emailed the council to see if this includes MH.
Update. The council reponded to let me know that all the car parks in Alloa can take a MH but the recommendation is to use the cp at the rear of Alloa Town Hall, off Marshill.