Yes it is possible to remove these from the drop down list, however you have to use the singlepage checkout in order for this to work. You need to copy the 2 sql statements below and execute them in host -> sql and ensure "execute as script" is selected, you also need to change the portal ID to the correct portal your store is located on. The below statements are correct for a portal with an ID of 2, once you have executed both statements you will need to go to host -> host settings and select "restart application", for the changes to be picked up:
declare @portalId int
set @portalId = 2
if not exists(select null from {databaseOwner}[{objectQualifier}CVStore_StoreAttributes]
where parentId = @portalId and name = 'CV_STORE_ACCEPT_AMEX')
begin
insert into {databaseOwner}[{objectQualifier}CVStore_StoreAttributes]
(parentId,name,value) values(@portalId, 'CV_STORE_ACCEPT_AMEX', 'False')
end
declare @portalId int
set @portalId = 2
if not exists(select null from {databaseOwner}[{objectQualifier}CVStore_StoreAttributes]
where parentId = @portalId and name = 'CV_STORE_ACCEPT_DISCOVER')
begin
insert into {databaseOwner}[{objectQualifier}CVStore_StoreAttributes]
(parentId,name,value) values(@portalId, 'CV_STORE_ACCEPT_DISCOVER', 'False')
end