If you do not have a fixed club, for example you are a freelance cricket coach who takes up temporary roles at various different institutions, your DBS application can be initiated by a County-wide user in your home County (or the County where you perform most of your work).
While it is possible to apply for a DBS without selecting a club on the online form, it is advised that you do select a club where possible as this affiliation in the system allows for easier communication between yourself, the club and club Welfare Officer and the ECB (should communication ever be necessary).
Your DBS application should therefore be made under the club with which you have most affiliation, even if the affiliation is only small. The club's Welfare Officer/verifier can initiate the application for you.
There are organisations/institutions which, while not being 'clubs' per se, have been set up in the system as such, with verifiers attached, so it is always worth checking to see if the organisation you are working for is set up in the system (you may do this by emailing firstname.lastname@example.org) and, if so, directing your initial request for a DBS in that direction. Two examples of organisations set up as clubs - or 'DBS branches' - in the system are 'Armed Forces' and 'London Schools Cricket Association'.