First of all, with rare exceptions the landlord would be responsible for safety related items such as railings, unless you are changing them only for looks. Also, on rental properties this sort of modification had better be approved and detailing who is paying for it and how reimbursed (if at all), in advance and IN WRITING, by the landlord.
You said nothing about what type of railing, if plain construction lumber or treated or architectural moldings, if lattice or slats, plain rectangular wood section or shaped, treated or stained or painted, level or inclined stairs also, etc. As you can see, a lot of variables.
The building code has changed a lot since the original was built, too - both with regard to strength and to child safety, so that increased cost about 100% over old-style railings.
Ballpark numbers, ASSUMING the deck fascia board is in good shape to fasten the posts to, is about $10-25/LF for standard wood railing (4x4 posts, 2x2 slats, higher price is for treated wood), $20-40/LF for plastic or architectural sections or metal railing with wood handrail. All-metal and glass or acrylic can run from about $50-500/LF, depending on how artisitic and art-deco you get (the more it looks like Hollywood, the pricier). Depends an AWFUL lot on your local timber and labor prices - in the deep south southern pine country wood and labor are cheap, so cost can be half that of the northeast or west coast.