Hope this helps date the image to within a gnats whisker. There is an image available on ebay here;
http://cgi.ebay.co.uk/LIVERPOOL-Technical-School-Tram-1903-PPC_W0QQitemZ390056852041QQcmdZViewItemQQptZUK_Collectables_Postcards_MJ?hash=item5ad1333a49&_trksid=p3286.c0.m14&_trkparms=65%3A12|66%3A4|39%3A1|72%3A1684|293%3A1|294%3A200
I know the links are long, I just hope they work. It is the same location, and style of post card (re ambiance), same type of open top tram too! I realise the photo could have been taken at anytime prior to Oct 1903, but note that the overhead cables are in place which means that it could not have been taken before 1898 according to Geoff's link. When did the open top trams begin to be covered in upstairs, as it seems they were eventually all covered up top as in this style, like a veranda.
http://cgi.ebay.co.uk/y9162-Liverpool-Tram-231-photo_W0QQitemZ360154318765QQcmdZViewItemQQptZUK_Collectables_Postcards_MJ?hash=item53dadec7ad&_trksid=p3286.c0.m14&_trkparms=65%3A12|66%3A4|39%3A1|72%3A1684|293%3A1|294%3A200
In 1905 some trams look to be covered up top. So I think it is fairly safe to say pre 1905.
http://cgi.ebay.co.uk/1905-pu-pc-Castle-Street-Town-Hall-Liverpool-Tram_W0QQitemZ310124521533QQcmdZViewItemQQptZUK_Collectables_Postcards_MJ?hash=item4834dca83d&_trksid=p3286.c0.m14&_trkparms=65%3A12|66%3A4|39%3A1|72%3A1684|293%3A1|294%3A200
Colour cards began in about 1907 and here is a card from after that time circa 1920, note the veranda's are still in use;
http://cgi.ebay.co.uk/LIVERPOOL-c-1920-PPC-LORD-STREET-TRAMS-SHOPS_W0QQitemZ160285430802QQcmdZViewItemQQptZUK_Collectables_Postcards_MJ?hash=item2551c19412&_trksid=p3286.c0.m14&_trkparms=65%3A12|66%3A4|39%3A1|72%3A1684|293%3A1|294%3A200
However by 1931 trams were being renovated and the whole of the upstairs was being covered as in this card of the type;
http://cgi.ebay.co.uk/Pamlin-Postcard-Liverpool-Corporation-Bogie-Tram_W0QQitemZ360124800918QQcmdZViewItemQQptZUK_Collectables_Postcards_MJ?hash=item53d91c5f96&_trksid=p3286.c0.m14&_trkparms=65%3A12|66%3A4|39%3A1|72%3A1684|293%3A1|294%3A200
The trams were renumbered and re-entered service. Even today, railway stock that is renovated is always given a new number to identify it from non-renovated stock.
The bubble bodied trams were introduced after WW2 as far as I can tell.
Hope these bits and pieces help at least a bit.
During this bit of digging I also came across this sad image of the end of trams in Liverpool;
http://cgi.ebay.co.uk/y9160-Liverpool-Tram-Last-Tram-Week-photo_W0QQitemZ290316565286QQcmdZViewItemQQptZUK_Collectables_Postcards_MJ?hash=item4398373b26&_trksid=p3286.c0.m14&_trkparms=65%3A12|66%3A4|39%3A1|72%3A1684|293%3A1|294%3A200
Unbelievable that they only lasted 60 years and the system as a whole 87, and yet after only 30 - 40 years after closure there has been talk of re-building the system. What goes around comes around eh?!
Interesting subject, I have enjoyed this one.
Philip