Does Solemnity prevent poison counters from being placed on a player by infect?

Solemnity states that players can't get counters. Poison counters are explicitly a type of counter placed on players, so Solemnity's replacement effect prevents them from being placed. This is confirmed by CR 122.1, which establishes that counters on players function the same way as counters on permanents — they are still counters.

Infect (CR 702.90) causes damage dealt to players to be represented as poison counters instead of loss of life. When an infect creature deals damage to a player, the game tries to place that many poison counters on the player. Solemnity (functioning as a replacement effect under CR 614.1) steps in and prevents those counters from ever being placed.

The player still 'takes damage' in a rules sense — it's just that the counters are replaced by nothing, so neither poison counters accumulate nor life is lost (infect damage to players doesn't cause life loss by default). The damage event occurs but has no visible effect on the player's life total or counter total.

Concrete example: Your opponent swings with a 2/2 Glistener Elf. It deals 2 infect damage to you. Normally you'd get 2 poison counters, but because Solemnity is on the battlefield, the replacement effect prevents those counters from being placed. You receive no poison counters and lose no life.

Note that Solemnity does NOT prevent the damage from being dealt — it only prevents the counters. Also, proliferate could still be used to add poison counters if a player already has some... except with Solemnity in play, proliferate attempts to add counters to players are also prevented (CR 701.27).