I'm assuming part of it is due to their exceptional naval capabilities, but what other reasons were there?
Well, many reasons. For one, as far as Europe goes, they are the closest to the Americas for colonization.
The Habsburgs also just gained control of it (Spain) through succession and with Naples, the Netherlands, Hungary and Bohemia also under their crown it was more than a little difficult to go against them militarily. Unless of course you are the Ottomans. So trying to pressure Spain and/or Austria was difficult especially since France had just spent almost a hundred years trying to get its land back and England and Denmark were also suffering a lot of instability. And Russia wasn't even Russia yet.
So of course Spain and Portugal had the best opportunity to turns its attention towards the Americas while everyone else wouldn't be in a position to really contest for some hundred years.
The reason this fell through should also be pretty understandable, its hard controlling overseas territory overseas territory already were under different administrative divisions for most countries, not just Spain. But during the period of instability suffered by Portugal and Spain during and after the Napoleonic Wars forced them to give up their two big colonies- Brazil and Mexico. The loss of Habsburgs in Spain also contributed a lot of problems continentally forcing them to pay more attention there.