This depends on the creature and will be fully up to your DM
In general, you become the full version of the creature when polymorphed, so if the creatures can have offspring, then two polymorphed creatures of appropriate sexes would be able to have offspring. Not all creature types breed normally though. For example, constructs and undead clearly do not, they are created; aberrations may have their own, sick ways to procreate (think, mind flayer, or beholder); devils are created from the souls of fallen mortals; monstrosities may be the result of magical experimentation gone awry rather than be born; if oozes mate is open to speculation. So, maybe you could breed a dragon, but you would not be able to breed a beholder (they are born out of the reality warping dreams of other beholders, and beholders try to avoid creating others).
There are a few other issues with this plan.
The first is that TP normally only keeps up for an hour, so your pals need to be OK to be polymorphed permanently to whatever creature you want them to be. You say they are willing, so let's assume this part works. More than a rules question, this is a question if your fellow players are interested in playing out your idea.
The second is that
The target's game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality. [...] If the spell becomes permanent, you no longer control the creature. It might remain friendly to you, depending on how you have treated it.
That is, if you transform them permanently, what they will do is up to them. Were those two PCs willing to have intercourse before you transformed them, so you can expect them to retain that personality attitude? Moreover, while they keep their overall personality and alignment, they are the new kind of creature now, their mental stats are changed, they are not just your former buddy. It therefore also will heavily depend on the creature.
Because the origin of this question was your interest to get access to the Gynosphinx's lair actions to time travel: Sphinxes in particular are a terrible choice for this (MM p. 280):
Divine Guardians. Sphinxes test the worth of those
who seek the treasures of the gods, whether forgotten
secrets or mighty spells, artifacts or magical gateways.
Creatures that choose to face a sphinx's test are bound
to that test unto death, and only those worthy will
survive it. The rest the sphinx destroys.
Some sphinxes are high priests of the gods that
create them, but most are simply embodied spirits,
brought into the mortal realm by devout prayer or direct
intervention. A sphinx maintains its vigil tirelessly, not
needing to sleep or eat. It rarely engages with others of
its kind, knowing no other life except its sacred mission.
Sphinxes are divine creatures whose aim it is to carry out their deities will, not hit it off with each other for a quick round of intercourse. They do not like to engage with others of their kind. Its not even clear if they procreate at all, as they are embodied spirits. (And the gyno in Gynosphinx stands for female, that is why they have a female head, like the andro in Androsphinx stands for male, which is why they have a male head. It is not clear if those two would have children, they are two different creatures).
So this is awful if you want a gynosphinx. It might work if you TP your friends into some creatures known for wantonness and kinkiness instead. Succubi, maybe? Although what those are really after are souls.
The third is that such a plan, even if it worked would likely take forever. Most larger creatures that do procreate have months of gestation period. Then you need however many years it will take for the children to mature. This is entirely outside of the scope of a normal campaign, that typically just takes a few months. (According to the DMG XP rules, it takes only about a month of full-time adventuring to get to level 20). Granted, there are some campaigns that have some downtime gaps interspersed, but I have - in my nearly 40 years of playing - yet to come upon a D&D-style campaign where years pass. (It is pretty common in Pendragon though).
The fourth and biggest one is that after all that effort, if the creatures you brought up will do what you want is entirely open to DM fiat. It would likely be a lot faster, if you want access to lair actions, to spend the time and do quests for an actual sphinx to get into its good graces. Or at least, if this will work as planned really comes down to get buy in from your DM.