Game Freak is just a tease sometimes.
Really, no recovery or boosting moves sucks but it's not necessarily the end of the world for Primarina. There's nothing wrong with being UU/RU material, which is currently where I can see it shining. It's got all around good stats, decent bulk, and good coverage, and I think if you slap a choice specs or life orb on it, it could be a pretty nice wallbreaker.
As other people mentioned, Liquid Voice Hyper Voice is probably best for doubles. While I would've loved for it to be an -ate type ability, in a way, it does still give Hyper Voice a boost by making it STAB. In singles, running Scald is probably the better option.
If I had to theorize a set, it'd probably be essentially a carbon copy of Sylveon's, in terms of item/evs/nature.
Primarina @ Choice Specs
Ability: Torrent
EVs: 252 SpA / 252 Spe / 4 Def
Modest Nature
- Scald
- Moonblast
- Psychic
- Energy Ball/Shadow Ball
Made this with UU in mind. Scald is STAB and has a chance to burn, Moonblast is STAB, Psychic hits poison types, and Energy Ball hits fellow bulky waters, even being 4× effective on Swampert. Alternatively, maybe Shadow Ball could be used for things like Metagross and Bronzong.
Course, we don't know for sure if Primarina will be UU, or what set with EVs to run until we playtest it. But I can see Primarina's moveset being something like that, even in other tiers.