What are some measures that could be taken to halt, or atleast slow, the decrease in slave populations?
Well as I said if you have the passage of the
Law of Free Birth (in 1871 it was, not 1867 - sorry, my bad) fail it would mean all children born after 1871 to slaves would still be slaves.
Perhaps Pedro II is overthrown after his
1867 Throne Speech calling for the gradual abolition of slavery?
Oh, and, do you think if they(CSA/Brazil) changed the terminology to 'indentured servants' that Britain would look the other way?
Can't really see the CSA changing the name for slaves. Having just fought a war to successfully preserve their states' rights to have slavery against the perceived threat of an abolitionist President I doubt they would go for a name change.
In any case, having Britain view the CSA (which has slaves) as a rival is essentially unavoidable given that Britain's position in the world was founded partly on trade and the CSA would be threatening that trade with slave labour. The planters and merchants in the West Indian colonies and India will be vehemently opposed to any good relations with the CSA and these people had some amount of influence on the British government (for instance it was these same classes which advocated that Britain take Canada as a war prize rather than one of the French islands (I think it was Martinique) after the Seven Year's War because they did not want to compete with yet another rich sugar colony for Britain's home market). You also have all the merchants and industrialists in Britain who would not be amused with the cheap, slave-made goods competing (and indeed undercutting) their own goods (and remember that these merchants, industrialists and factory workers are all voters in Britain....nobody in the CSA is a voter for the purposes of the British general elections).
Besides, I think it would make for a more interesting TL to have the CSA navigate the tricky diplomatic waters of relations with the UK, USA, France, Haiti, Liberia and Spain.
Hmmm. Why not just grab a (useful) piece of Africa and make a "Black Nation" out of it? You know, to feed the CSA with cheap, cheap rubber and the like.
That would be like playing with lit dynamite. In fact that would probably be one of the fastest ways to get the CSA involved in a war with the USA, Britain, France and Germany. Britain would probably just outright sink any CS ship heading to Africa if the CSA tried to actually grab a piece of Africa and France would support that effort. And with the Royal Navy likely to be many magnitudes of order larger than any Navy the CSA could field then the CSA would probably end up losing any Caribbean possessions and being subject to a blockade akin to what it experienced in OTL from the Union Navy (and which I suspect it did not really experience in the TL you are planning). Any Confederate attempt to grab territory in Africa would arouse suspicions that the CSA was trying to bring back the slave trade under the radar.
As a nation which encourages free trade in its own constitution the CSA is likely to prefer obtaining cheap, cheap rubber through free trade and to use parts of Africa (and maybe Haiti) as a dumping ground for troublesome and "excess" or "abandoned" slaves after the Boll Weevil sweeps through the South.