You can have the GPS as primary nav and no alternate if you have 2 TSO129 units. If you have a single TSO145/146a GPS it can be primary nav and no alternate.
Not quite true. According to AIP if you only have TSO129 units you still must carry an ADF or VOR receiver.
For alternate requirements, AWK/PVT are fine with just one TSO129; CHTR/RPT you need 2 TSO129 units as you say. You still need two units for CHTR/RPT even if they're TSO145/6.
Edit: Two Dogs below is right: 129 can't be used to satisfy alternate requirements in any case, but you still need 2 145/6 receivers.