What roof do you have? Do you have a sunroof/moonroof? What pop outs are you referring to? Might they be aftermarket and added by the previous owner?
I have a 1992 Toyota Previa LE with no roof rack and no sunroof/moonroof. The only suggestion that I have seen so far is to retrofit a roof rack from another vehicle, which is the most likely idea I will follow after since there is a salvage yard that sells them for about $25.
An aftermarket solution that I believe would work is Rhino Rack's RTV Tracks.
Here's a YouTube Video link to see how they install:
Besides that, I do not know of another simple or straightforward solution. There seems to be some roof racks that were sold outside of the US for non-US Previas that would probably work, but it may be difficult to source them to the US.
Here's a blog that showcases some roof rack options for Previas:
As far as the Toyota OEM roof rack for the Previa there is the requirement to have rivets in the roof. I actually was dismantling a Toyota OEM roof rack and saw the rivets and did not know how I would install the rivets on my Previa, so I gave up on it. Now thinking back on it, I probably could have learned how to install rivets... I'll have to wait to find another Previa with a Toyota OEM roof rack.
As of now my best bet is to search the salvage yard and try to see if there's a roof rack I could retrofit onto my Previa. I was thinking that the first gen Toyota Sienna's roof rack may work. Or possibly the Honda Odyssey. Someone on ToyotaNation.com suggested an old Chevrolet Suburban roof rack, which I may look into.
I recently got my first Previa and I am truly loving this vehicle. Such a smooth ride and amazing handling for a vehicle of this size!