Yes. You don't have to have them in a different db either if you don't want to. You can store individual tables in different table spaces and table spaces map to any place you want on any disk.
I'm puzzled though that your CA is taking 20-30 seconds. I have CA and about 20 other states loaded and CA doesn't take that long. Your stats may be out of date or you are missing indexes, so you might want to run this covered in step 9 of the manual - http://postgis.net/docs/manual-2.3/postgis_installation.html#install_tiger_geocoder_extension
vacuum analyze verbose tiger.addr;
vacuum analyze verbose tiger.edges;
vacuum analyze verbose tiger.faces;
vacuum analyze verbose tiger.featnames;
vacuum analyze verbose tiger.place;
vacuum analyze verbose tiger.cousub;
vacuum analyze verbose tiger.county;
vacuum analyze verbose tiger.state;
vacuum analyze verbose tiger.zip_lookup_base;
vacuum analyze verbose tiger.zip_state;
vacuum analyze verbose tiger.zip_state_loc;
Regarding putting tables in different table spaces, first you need to create a table space on your ssd.
1) Create a folder to house the table space and make sure the postgres process has full permission (preferably owns it)
CREATE TABLESPACE tiger_big LOCATION '/path/to/folder';
If you are on windows, You do something like 'D:/foldertohouse' for the path.
Next you can move tables to that table space. For example to move the CA ones would be
ALTER TABLE tiger_data.ca_addr SET TABLESPACE tiger_big;
ALTER TABLE tiger_data.ca_edges SET TABLESPACE tiger_big;
ALTER TABLE tiger_data.ca_faces SET TABLESPACE tiger_big;
ALTER TABLE tiger_data.ca_featnames SET TABLESPACE tiger_big;
ALTER TABLE tiger_data.ca_place SET TABLESPACE tiger_big;
There are some others for CA, but you get the idea