'Naturally' Germany, Austria-Hungary and Turkey would be interested in anyone joining their cause.
This is not about who ended up in 1918 being at war with Germany, Austria-Hungary, Bulgaria and Ottomans. This is about all those considered by one side or the other as potentially siding with "them" from 1914–1918. And this list of attempts is surprisingly long as is the list of successes in that direction short.
Besides Mexico, this includes Italy, Switzerland, Norway, Netherlands, Luxemburg, Romania, Greece, Venezuela, Afghanistan, Abyssinia, Sweden, Japan.
Given the German initiatives in the far East, the "offering" of German colonial possessions might also indicate that the United States would have to be included (however theoretical and unsuccessful that turned out). That view of dreadful potentialities was initially shared by the British, as they were quite keen to restrict some of their naval blockade tactics so as not to anger the Americans, who preferred trading with all sides involved at the beginning.
The German plans and ambitions were fulfilled with Bulgaria's entry into he Central Powers alliance.
Wooing Romania was a constant throughout the war. Not really successful.
Hampered by tactical considerations potential allies like Sweden, Netherlands or Switzerland were seen as much more useful if they stayed 'neutral' so as to continue trade. In the case of Switzerland the neutrality was at times called into question: with the Grimm–Hoffmann affair. Sweden was equally sympathising with Germany, for the most part, and the busy man Zimmerman did offer a few perks as well.
In the wider picture of the globe German hopes were directed at Mexico, Venzuela in South-America, at Abyssinia and Afghanistan in Africa and Asia.
In the height of colonialism, not really many independent countries were left on the map, that did not clearly see more strategic value in staying neutral or siding with the Entente.
Although not explicitly independent countries for this purpose it just has to be noted that just like all those nationalities in the Russian Empire (as excluded from the question) every Muslim was considered a potential ally and the Germans tried to explicitly call them to Jihad against their Western oppressors. This hoped-for alliance from Morocco to Pakistan would then have to be expanded to India, as the Hindu–German Conspiracy falls into a similar league.
Perhaps tangential to the aim of the question: but with Japan Germany really hoped to come to an early end of official hostilities and negotiated in earnest what was mere tactics for "offering peace" in Europe.
As this was not "promised independence" one might also consider the fact that the Ottoman Empire engaged in a frenzy of diplomatic activity, mainly after the Russian Revolution and attempted to gain allies against the British and Russians.
And depending on viewing angles, the Germans also offered Greece assistance against the allies forcing them into their camp, albeit with some imperial Prussian elegance and decorum:
On the Central Powers' side, on 29 November 1915 Falkenhayn had publicly threatened that if Greece could not neutralize the Allied and Serbian forces in its soil, the Germans and their allies would cross the border and do it for them, and on 10 December, the German Foreign Ministry reacted to the new agreement between Greece and the Allies regarding their armies in Macedonia by demanding the same rights of free movement in Greek territory. To these demands, the Greek government answered on 22 December that it would not actively oppose a Central Powers invasion of its territory, provided that the Bulgarians did not participate, or at least stayed out of the cities, and the command of the operations was in German hands; that Bulgaria issued no territorial demands, and that the Central Powers forces would withdraw once their objectives were met; and that the Greek authorities remain in place.
- Holger H. Herwig: "German Visions of Empire in Venezela 1871–1914", Princeton University Press: Princeton, 1986.