What I found worked:

I found this worked to install geopandas.

!conda update -n base -c defaults conda --y
!pip install geopandas
import geopandas as gpd

It looks like Python 2.x is no longer available, only 3.x. I'm getting the same error as described in Stephen Mc's message.

Geopandas is a definite need for spatial data science ...

Ultimately, I would like to do spatial joins like those described here:

http://geopandas.org/mergingdata.html

when I import geopandas, I get this

OSErrorTraceback (most recent call last)
<ipython-input-4-f8b81fe8ca07> in <module>()
----> 1 import geopandas as gpd

/resources/common/.virtualenv/python2/lib/python2.7/site-packages/geopandas/__init__.py in <module>()
----> 1 from geopandas.geoseries import GeoSeries
2 from geopandas.geodataframe import GeoDataFrame
3
4 from geopandas.io.file import read_file
5 from geopandas.io.sql import read_postgis

/resources/common/.virtualenv/python2/lib/python2.7/site-packages/geopandas/geoseries.py in <module>()
14
15 from geopandas.plotting import plot_series
---> 16 from geopandas.base import GeoPandasBase
17
18 OLD_PANDAS = issubclass(Series, np.ndarray)

/resources/common/.virtualenv/python2/lib/python2.7/site-packages/geopandas/base.py in <module>()
13
14 try:
---> 15 from rtree.core import RTreeError
16 HAS_SINDEX = True
17 except ImportError:

/resources/common/.virtualenv/python2/lib/python2.7/site-packages/rtree/__init__.py in <module>()
----> 1 from .index import Rtree
2
3 from .core import rt
4
5 __version__ = '0.8.3'

/resources/common/.virtualenv/python2/lib/python2.7/site-packages/rtree/index.py in <module>()
3 import pprint
4
----> 5 from . import core
6 import ctypes
7 try:

/resources/common/.virtualenv/python2/lib/python2.7/site-packages/rtree/core.py in <module>()
123
124 if lib_name is None:
--> 125 raise OSError("Could not find libspatialindex_c library file")
126
127 rt = ctypes.CDLL(lib_name)

OSError: Could not find libspatialindex_c library file

If I understand this feature request correctly, the goal is to be able to use GeoPandas to work in Jupyter notebooks. I hope I got this right.
I tried installing GeoPandas in a Python 2 Jupyter notebook. Everything seems to have worked and I did not get any messages about unsatisfied dependencies:

!pip install geopandas

Collecting geopandas
Downloading geopandas-0.2.1-py2.py3-none-any.whl (199kB)
100% |████████████████████████████████| 204kB 3.2MB/s
Collecting pyproj (from geopandas)
Downloading pyproj-1.9.5.1.tar.gz (4.4MB)
100% |████████████████████████████████| 4.4MB 186kB/s
Requirement already satisfied (use --upgrade to upgrade): pandas in /usr/local/lib/python2.7/dist-packages (from geopandas)
Collecting fiona (from geopandas)
Downloading Fiona-1.7.1.post1-cp27-cp27mu-manylinux1_x86_64.whl (39.7MB)
100% |████████████████████████████████| 39.7MB 20kB/s
Collecting shapely (from geopandas)
Downloading Shapely-1.5.17.post1-cp27-cp27mu-manylinux1_x86_64.whl (8.3MB)
100% |████████████████████████████████| 8.3MB 105kB/s
Collecting descartes (from geopandas)
Downloading descartes-1.0.2-py2-none-any.whl
Requirement already satisfied (use --upgrade to upgrade): python-dateutil in /usr/local/lib/python2.7/dist-packages (from pandas->geopandas)
Requirement already satisfied (use --upgrade to upgrade): numpy>=1.7.0 in /usr/local/lib/python2.7/dist-packages (from pandas->geopandas)
Requirement already satisfied (use --upgrade to upgrade): pytz>=2011k in /usr/local/lib/python2.7/dist-packages (from pandas->geopandas)
Collecting cligj (from fiona->geopandas)
Downloading cligj-0.4.0-py2-none-any.whl
Collecting click-plugins (from fiona->geopandas)
Downloading click-plugins-1.0.3.tar.gz
Collecting munch (from fiona->geopandas)
Downloading munch-2.0.4.tar.gz
Requirement already satisfied (use --upgrade to upgrade): six in /usr/local/lib/python2.7/dist-packages (from fiona->geopandas)
Requirement already satisfied (use --upgrade to upgrade): click>=4.0 in ./common/.virtualenv/python2/lib/python2.7/site-packages (from cligj->fiona->geopandas)
Building wheels for collected packages: pyproj, click-plugins, munch
Running setup.py bdist_wheel for pyproj ... - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ | / - \ done
Stored in directory: /home/notebook/.cache/pip/wheels/85/dd/2f/d1ed07a507c7adb330cda0afcc96cae8e9abb4d85bbb788bdf
Running setup.py bdist_wheel for click-plugins ... - done
Stored in directory: /home/notebook/.cache/pip/wheels/70/d7/3d/188128669f2aa42f6008217d9e2e6826d398dc3e361c0fcb75
Running setup.py bdist_wheel for munch ... - done
Stored in directory: /home/notebook/.cache/pip/wheels/09/dd/7e/90fd2e7735566f3b6d7faad334a6b7b1ae0b8b5601616d7086
Successfully built pyproj click-plugins munch
Installing collected packages: pyproj, cligj, click-plugins, munch, fiona, shapely, descartes, geopandas
Successfully installed click-plugins-1.0.3 cligj-0.4.0 descartes-1.0.2 fiona-1.7.1.post1 geopandas-0.2.1 munch-2.0.4 pyproj-1.9.5.1 shapely-1.5.17.post1
You are using pip version 8.1.2, however version 9.0.1 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.

I understand that Rtree is an optional package so I went ahead and installed it as well. And it also installed just fine.

!pip install rtree

Collecting rtree
Downloading Rtree-0.8.3-py2-none-any.whl
Requirement already satisfied (use --upgrade to upgrade): setuptools in ./common/.virtualenv/python2/lib/python2.7/site-packages (from rtree)
Installing collected packages: rtree
Successfully installed rtree-0.8.3
You are using pip version 8.1.2, however version 9.0.1 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.

Does that mean that this feature request is no longer needed?