If a persist creature is used, it does not have a -1/-1 counter on it.
Otherwise, if an undying creature is used, it does not have a +1/+1 counter on it.
Steps
Activate
Bloodflow Connoisseur by sacrificing the persist or undying creature.
When the creature dies, its persist or undying ability triggers, returning it from your graveyard to the battlefield without a -1/-1 counter or a +1/+1 counter on it due to
Solemnity.
Resolve the
Bloodflow Connoisseur ability.
Repeat.
Notes
If you wish to get infinite +1/+1 counters on
Bloodflow Connoisseur, instead do not resolve its abilities, and then remove
Solemnity from the battlefield. Then, resolve the abilities to get the +1/+1 counters.