When filing by mail, there's only one place on the 1040 signature line to write a PIN. But we're married filing jointly and we both have PINs. Where do we write the PINs?

You only place the IP PIN for the person who is listed first on the return when you are filing by mail.

Here are the instructions from Form 1040 for signature section and IP PIN -

"If you are filing a joint return and both taxpayers receive an IP PIN, only the taxpayer whose social security number (SSN) appears first on the tax return should enter his or her IP PIN. However, if you are filing electronically, both taxpayers must enter their IP PINs."

https://www.irs.gov/pub/irs-pdf/i1040gi.pdf  (page 76)

I actually found my own answer in the 1040 instruction PDF supplied by the IRS.

If you are filing a joint return and
both taxpayers receive an IP PIN, only
the taxpayer whose social security number
(SSN) appears first on the tax return
should enter his or her IP PIN. However,
if you are filing electronically, both taxpayers
must enter their IP PINs.