Well the issue I see is what kind of butterflies are you willing to unleash?
Haiti I'll tell you is going to be a non-starter. Best bet is to curve German investment there by replacing it with American investment. The only problem there is that the USA is not particularly well meaning towards people of African descent. Germany got its influence by being more willing to integrate into Haitian society more than any other European group. They often ended up marrying into the better off Mulatto Haitian families to secure their assets.
Haiti was investment starved up to about 1906. So they ended up controlling the vast majority of Haitian international trade. I say start up the Haitian American Sugar Co early and possibly invest in starting a cacao growing plantation as that has constantly increasing demand. Buying out the National Bank of Haiti/Treasury will likely cause a wave of anti-Americanism again but I doubt many would realize this at the time as it isn't something commonly known to people who are not Haitian History buffs. It might be hard but get an agreement where the US is responsible to protect the country from foreign invasion and get it to give up a standing military to turn it along the lines of Costa Rica.
The Dominican Republic is only 30 years away from a period when it wanted to join the USA so it should be easier for them. Also it is heavily in debt to many nations including the USA. It was the whole reason the Roosevelt Corollary to prevent the creditor nations from having their warships attack the DR which at the time was still called San Domingo. The US could instead offer annexation and protection with the USA taking on the debt while stating the corollary. If the government of Carlos Felipe Morales Languasco (the former General who overthrew the last usurping president in the 4th revolution since 1899 I believe) refuses well it wasn't an offer he can refuse. The Jimenistas faction which he betrayed to take power will need to be dealt with less they lead another revolt this time against the US. I say put them on trial for destabilizing their own country and throw in some of the Horacistas faction too who won't go along but treat the public very well. There is in fact a detachment of Marines in San Domingo from March to April. Then it might be a good idea to establish a facility and get an agreement towards a single military.
Cuba needs Guantanamo Bay base to either not be the only US base or be bigger.
In Nicaragua the US has deployed US troops to occupy Bluefields on three occasions up to 1903. If things progress as in OTL then expand US interest in Nicaragua and build the competing Canal. If not then get basing rights and build many bases and expand a Hong Kong like American enclave but treat the local population well with plenty of education. Later when there is revolution in the country move things towards a US friendly dynamic by helping the people and place the whole country as a protectorate with a referendum on closer relations with the USA.
For the money the US will need to make some infrastructure and economic changes itself. Holt tractors were quite the development and surprisingly the US was the only country not to make the connection to the possibility of tanks if that can change it will end up better off when wars come around. Possibly make better use of airships for shipping till the air plane is better designed. Get the federal reserve system modernized. End the serfdom of African Americans and crush the restore Slave Powers of the Dixicrat South.
See if you can get agreements to get these countries not to have standing armies. Mutual Defense Treaties, Associated States so they can join the US military, or just pay them not to maintain armies also.
Get these nations really integrated into the US economy, politics, culture, and travel similar to Mexico, Japan, or the Philippines today. Large immigrant communities on both sides will help and bases/facilities/universities/academies in these countries will create American expatriates. It will also mean more investment in infrastructure to support their living there as in power plants, water treatment, roads, and schools.
All these tell that if you want growth the USA needs internal change. In 1903 you are just a few years too late to prevent Jim Crow starting to entrench itself so you will have to root it out. Progressives have the motivation and momentum so it may be possible. The best way is to create a wealthy upper class among Southern African Americans so they can afford to compete and fight back. Now this should be possible if extremely difficult.
One effort could be to get the likes of Ben Tillman, and William Bryan Jennings out of the USA for a time discussing treaties or as ambassadors and such. If they happened to get sent to a rather unstable region of the world and something happened to them all but a shame. Buy out any property they own and do your best to bankrupt them.
Now if they had some luck or knowledge of the future you could get some groups to start co-ops on oilfields getting loans from banks in other countries or the federal government.
