The public car park for Galloway House Gardens is here.

It costs either £3 or £4 per car per day,  the operators' website is ambiguous.

It is open March 1st to October 31st, 9am to 5pm. 

Sources:

https://gallowayhousegardens.co.uk/ (front page) says "We charge £3 for parking"

https://www.gallowayhousegardens.co.uk/index.php?page=visitor-advice says "The arboretum and woodlands are open from March 1st to 31st October between the times of 9:00am and 5:00pm." and "The charge for car parking meter is £3.00 per car per day."

https://www.gallowayhousegardens.co.uk/index.php?page=contact says "Car park charge is just £4.00 per car per day."

To verify land use, this is where the car park is in google maps aerial photography:
https://www.google.com/maps/@54.7783492,-4.3707317,74m/data=!3m1!1e3