Hi Oli,
You could easily spend 2 days in Costanera Sur - it's a big and diverse place with plenty of great birds. For a couple of different species (i.e. Rufous-sided Crake) you could consider hopping on the local commuter train to Acassuso. Walk down to the river to visit Ribera Norte which has riparian woodland and a viewing platform.
I've not visited Otamendi, but have heard the same safety warnings from local birders - maybe visit with a guide or local group?
Personally, with two days I would do the following: early start along the Laguna de Los Coipos (outside Costanera Sur, which only opens at 8 am). The northern half is best and has both Masked Duck and Lake Duck. Then spend most of the morning and early afternoon in the reserve proper. Next, pick up a rental car (plenty of places downtown) and drive north. Quick visits to Vicente Lopez and Ribera Norte (which closes 6 pm) should give you some additional species you won't get in CS. The traffic is a little crazy in downtown BA, but eases up once you get past the airport. From there, head out of the city to Zarate and then north to Ceibas in southern Entre Rios (easy motorway drive, about 2 hours). Stay at the Rio de las Aves lodge which caters for birders and has both comfy and cheap bunk accommodation (and great food!). Their private reserve has an impressive bird list and Ceibas is one of the best birding spots in the entire region. Do the lodge grounds in the morning (bring waterproof boots or wellies!) and you should have 80-odd species. After lunch do a slow drive around the 'Ceibas loop' for things you've missed, and you can be back in BA for a late dinner. I know you're not keen on getting a car, but in this case it's worth the bother!
The whole place is great for birds; I found 136 species in BA and Entre Rios, but if you're Noah Strycker you can get 146 on a single day in Ceibas
https://www.audubon.org/news/birding-without-borders-day-14
Have a great trip and let me know if you need any detailed info!
Joost