There are many different kinds of cones, and each type has different options.
For run-of-the-mill AA5 speaker (cheap), they usually crack rather than tear. A soft-set hot-melt glue across the tear usually does it. Do a zig-zag first, then cover the tear completely. Hotter the better, so the glue soaks into the paper. By the way, there is nothing wrong with hot-melt glue with silicon admixtures if applied hot enough. Other than the cost. And of one uses archival-grade glues, oxidation is greatly reduced. It's only money - and six sticks will do, likely, 120 speakers, so the cost-per is minimal.
https://www.gaylord.com/Preservation...Pack)/p/636315
Most cone paper is very hard to retain rigidity in use. What goes back needs to be able to accommodate the hard paper so as not to tear again on the seams.
This stuff is ideal:
https://www.amazon.com/Lightweight-N...=fsclp_pl_dp_3
And a lifetime supply for a few bucks is not hard to take.
None of these beat professional reconing, but many applications are not worthy of that expense
Peter Wieck
Melrose Park, PA