How can I get get a fellow federation member to convert their tributary into a member of our federation in Stellaris?

Solution 1:

You have a few options here but none of them are great nor sure-fire:

Option 1: Wait them out. It is possible for the overlord to transform tributary status into a protectorate or vassal, but only if the overlord is big and influential enough. Since you want the tributary to join your federation, I doubt this is the case, but nevertheless, waiting for them to turn into a vassal and being integrated is an option .. be prepared to wait a few hundred years, though.

Option 2: Support Independence. Also unlikely to result into actual war, since it's rare for the AI to be disgruntled enough to actually declare war over this. Then, in the rare case that this works, invite the former tributary. Most likely the former overlord will have something to say about this, however, as war tends to not be great for friendships.

Option 3: Lone Wolf it. Unfortunatly your best chance for success is ditching that circlejerk keeping your galactic ambitions in check! Without having to wait for an AI that is unlikely to act you can declare war on your former ally to get your new friends the freedom they so long for (or steal them for yourself). After you've obliterated them you execute the wisest move in your arsenal: feigning ignorance. Start treating your allies like buddies again and I'm sure their tiny tentacled xeno-brains will have forgotten all about it in no time to open the door to letting you back in.

Option 4: What do you mean, attacking allies? Tributary overlords are in no way obligated to aid their tributaries in a war. Liberating / Conquering the planets of the tributary will slowly but surely allow you to get them to join your cause, altough I'm not sure what the rules are for declaring war on tributaries of federation members.

In short: There's no great way to accomplish this -yet-.

This is what the Stellaris Wiki has to say about tributaries.