How much coin could the Romans afford to sink into Arabia?
At this point, quite a bit - prior to the Roman-Sassanid Wars the east was pretty bloody wealthy - divert some of that wealth. I'll have to look into some more discrete numbers though. Might be worthwhile to levy a small tax (say for the privilege of religious freedom? Roman-Jizya?

) They would probably be able to afford to reduce army numbers if it went to plan, as the Tanukids would protect their long desert border - long term savings there in exchange for the short term costs.
The Sassanids had their own powerful Arab allies, the Lakhmids, and Rome / Byzantium had various Arabian allies, too. They proved to be significant, but not overwhelmingly decisive in the Roman-Sassanid wars.
The Lakamids and Ghassanids were really only in N.Arabia, and as a result had much lower manpower and less wealth than a client state / friendly Christian power across Arabia. That would be a much more powerful ally to have.
I´ve been putting some effort into considering such options, too, for my Alexandria-based Roman split-off republic of the 3rd century CE ff.
The temporary conclusion I´ve come to is:
To unite (pre-modern) Arabia, you need a powerbase both among the clans of the desert, and in the relatively fertile South, which was of utmost maritime importance for Mediterranean-Indian trade. The first to achieve this were the Muslims, and the example shows that a unified Arabia is unlikely to be just Rome`s puppet.
I'd agree with most of this, but the important thing is that the Tanukids, apart from being long-term Foederati, if there is no reason for their revolt due to Valens - have had good long term relations with Rome, which is also Christian. The Tanukids were notably zealotic. I would expect them to prefer to ally with Christian Rome rather than the Zoroastrian Persians. They aren't likely to be a puppet forever - but certainly have a joint interest in corralling the Persians in their long term geopolitical strategy. Even if they did have to fight a war and split spoils, Rome may want Mesopotamia - but if the Tanukids get the coast and control of the Spice Trade - that is a pretty good deal for both sides there. In addition - if they are powerful enough, they could certainly reach a diplomatic arrangement where the Patriarch of Jerusalem leads their church - and is part of the Pentarchy, linking them to the Emperor in a religious organisation.
Everything else will be temporary and fragile, as OTL`s Roman-Arabian alliances were, too. There`ll always be someone who is willing and able to fight for Roman money, and there`ll always be someone else who is willing and able to fight against the Romans for Sassanid money.
Hence the Tanukids, relgiously devout/zealotic - and tied to the Christian Emperor. That combined with long term trade, there can be long term co-existence there, and the Tanukids can focus on expansion over the seas, without having to fight their major trade partner. A lot of beneficial ties that make cutting them and fighting for territory reckless and likely to cause rebellion with the wrong cause.
A strong federation only in Northern/Central Arabia, which could not stand by itself economically and thus depended on a partner like the Romans, sounds tempting, but what would keep them from meddling farther South, where Sabaeans, Himyarites, Hadramautians and even Aksumite vassals quarrelled with each other and where half-decent land and a lot of wealth was to be gained?
That was kind of my point - The Romans might intervene for a diplomatic solution regarding Aksum, or take over Aksum in Africa whilst the Tanukids take Arabia - but you'd have the Tanukids standing on their own once they had that. Strong, but not as strong as a Rome that isn't exhausting themselves on Roman-Persian wars of futility. It'd probably be a 2nd rate power until it focused on the Indian Ocean - where it would thrive.
Now is it destined to be happy forever, unlikely - there could certainly be a war or series of wars if either side becomes particularly dogmatic (hence why I'd rather the Pentarchy included a pro-Tanukid member, more likely to promote pluralism that way). Even if the Romans consider it a bad decision in the long term to pay the Arabs to unite, they wouldn't suffer the loss of Syria and Egypt ITTL, which makes it a pretty good opportunity cost.
Now the logistics of the Tanukid Conquest of Arabia is a question I haven't considered, so that would certainly be something to think of.