The below extract from the St John's Ambulance Museum website indicates that members of that organisation do recieve Coronation and Jubilee medals. However as they are a gift of the sovereign they are only awarded to a very limited number. It doesn't indicate how individuals are nominated to recieve one.
If SJA get them it is likely other volunteer organisations also get them on a similar criteria.
HM Armed Forces and designated Emergency / Public Services seem to get them on a relatively generous scale.
'The last coronation medal specifically for St John Ambulance was issued for George V’s Coronation on 22nd June 1911. After this event, the criteria for awarding Coronation and Jubilee medals also changed. No longer were they to be given to those who served at the event, but instead they have subsequently been awarded as an honour or souvenir to select individuals or groups. A few representatives from St John Ambulance have been awarded each of the subsequent medals but it does not necessarily mean that they participated in any festivities. These medals have been awarded to members of the military, members of the Royal household, government officials, mayors and the police among others. Around 300 members of St John Ambulance received the Elizabeth II Coronation Medal in 1953 and subsequent awards have been made to individual members on the occasions of her silver, gold and diamond jubilees.'