There is no MODIS data covering the entire neotropics (that´s quite a large area), but you can download several NDVI tiles from the MODIS data archive. I suggest you use the reverb.echo website (EOSDIS):
http://reverb.echo.nasa.gov/reverb/
There you can draw either a polygon around the area you want or even upload a shapefile covering your desired extent. Then search for the MODIS NDVI product of your choice, set the time span and then look what´s there. I guess a lot of tiles. You will then have to modify all of them using the MRT tool (= MODIS reprojection tool). This allows you to preproject and merge all images in one folder into a coordinate system e.g. UTM or geographic coordinate system.