Louis XVI, Charles X and Louis-Philip I did not lose their throne because they were conservatives that opposed liberal revolutionaries but because they refused to order the use of force to crush sedition.
While Louis XVI did lose his throne because he refused to use force when he got the chance, that's definitely not the case of Charles X...
The 1830 Revolution started with riots and barricades built in Paris and the army, under the commande of Marshall Marmont, was sent to restored order. The situation degenerated so much Charles X even declared Paris in a State of Siege. Shots were fired and fighting did happen throughout the city for three days (hence the nickname of
Trois Glorieuses given to the 1830 Revolution). So Charles X didn't fail because he refused to use force, he failed because he horribly handled the situation... Which isn't surprising because the man was highly reactionnar and with very little aptitude at compromising...
Since Louis XVIII’s wife Marie Joséphine of Savoy had died in 1810, we can have him remarry before the Restoration. Should the child be a girl, we could have Louis XVIII propose that the Chamber of Deputies abolish the Salic Law (Louis XVIII foresaw how the potential reigns of Charles X and Don Carlos would end and wanted to avoid that scenario at any cost). Assuming Louis XVIII manages to amend the succession and his daughter (we can call her Marie) becomes Queen, she would in a position analogous to Louis Phillippe in OTL since the Legitimists will favor the Artois line (OTL Charles X and his descendants). Marie would also need a husband who’s moderate and would mostly stay out of politics.
There is an issue with making this happen though. To start off, Louis XVIII was already 55 when his wife died: an old monarch in exile with no secure throne thus has little chance of securing a second marriage. Then, there are the reasons for which Louis XVIII choose not to remarry, which I personnally don't know: his age probably played a factord, the feelings he had for his wife (if he had any), etc... You'd need to thoroughly check those to see how likely he would be to consider remarrying.
Finally, there is the timing. Marie-Jospéphine of Savoy, Louis XVIII's wife, died on November 13, 1810. Louis XVIII died on September 16, 1824. That's a short 14 years gap, meaning any child born to Louis XVIII from this hypothethical second marriage would likely be underaged... Thus there would be a need for a Regency. And even if the regency's short (unless reformed, the majority of French Kings was still at 13), that leaves a young inexperienced King on the throne in a rather troubled era...
Are they going to pick the seniormost Spanish Bourbon, or simply the one they like the most?
Tradition would dictate the choice of the senior Bourbon.
Also, if the Spanish Bourbons are unacceptable to them, could they try installing someone from the illegitimate Capetian branch of Bourbon-Busset as the new French King instead?
It's possible but there have always been troubles around legitimizing Bastard lineages and integrating them into the succession. Louis XIV tried to have two of his illegitimate sons included in the succession in his will, but that ended up being broken by Parliament. We're a century after that of course, but I think some minds would still not like the idea, unless there no longer was any other option.
In addition to this, if other European powers intervene in order to crush a French republic in 1830, who exactly are they going to put in power in France? Given their monarchist inclinations, they'd have to find some monarch for this role--a Spanish Bourbon, perhaps?
The European powers would probably pick likely someone suitable for them and that could calm the situation. A Spanish Bourbon could work on the condition they don't see a personnal Franco-Spanish Union in this and if they are willing to repel Utrecht.
The other monarchical option I see is not a Bourbon... It's Napoleon II. The Austrians probably wouldn't have a problem with putting him on the throne since he's a prince of theirs by this point. Trouble is that it's basically putting Napoleon's son on the throne and that might cause concern.
By the Treaty of Montmartre in 1662, the House of Lorraine was named as next in line should the Bourbons die out. And by the 19th century, the only extant branch of the House of Lorraine were the Holy Roman/Austrian emperors. So that would mean either a son of HRE Leopold II (
https://en.wikipedia.org/wiki/Leopold_II,_Holy_Roman_Emperor#Issue) or a son, or grandson, of Austrian Emperor Francis I.
A problem with that reasonning is that we most likely end up with a foreign prince on the French throne... Which is kind of a big "no no" for France. I mean, the Hundred Years War mythos kinda build itself around the idea that it was Kicking the English out of France... So I don't see an austrian prince being well accepted.
Unless we're talking about the Duke of Reichstadt. But that's because he's not just the grandson of Francis I... He's also Napoleon's only son.
Louis XVIII was sexually impotent. Most historians agree on this.
So he won’t remarry.
But if you made him not impotent and have but a girl, I still don’t buy the abolition of the Salic Law.
Ferdinand VII was able to abolish the Salic Law because it had been quite recently imported from France by the Bourbons (barely a century).
At that time, the Salic Law had been the succession law to the throne of France for 5 centuries. It was so deeply entrenched in people’s minds that Napoleon also established succession rules in favor of the male lines.
The counter-argument to this would be that Times Change and Necessity makes Law.
It's true that Salic Law had been around for a long time but the situation could call for it. Furthermore, in the context of the XIXth Century, changing the succession law doesn't seem such an implausible task to undertake. I mean, France had already experienced its Revolution and went from an "Absolute" Monarchy to a Constitutionnal Regime.
And in that particular case, we're also facing a very disminished French Royal Family that is on the verge of dying out in the male line. And with no clear successor should that happen. So opening to female lines for the first time might be more of a necessity to expand the number of available legal heirs...