I am trying to find the correct translation for, "humbly yours in Christ" to put at the end of a letter. Would the translation "humilitate tua in Christo" be somewhat close? I have just recently begun studying Latin. Thank you very much for your help.
Though humilitas / humilis was mostly negative in classical Latin, it acquired its positive sense as a Christian virtue as early as the Vulgate (Matthew 11:29; James 4:6), Augustine (Confessions I.11) and certainly by the time of Aquinas (Summa Theologiae II-II, q. 161). This has a lot to do with the Christian emphasis on what Alasdair MacIntyre calls the "virtues of acknowledged dependence": whereas Aristotle only had the vice of pusillanimity, Aquinas acknowledges not only the vice but also the virtue of humility.
Another prefatory remark: the classical way of composing Latin letters (followed by authors as diverse as Cicero, Seneca, Petrarch, and Erasmus) is to name the sender and recipient at the beginning (e.g. "Seneca Lucilio suo salutem") and then to have a valediction at the end, often with the time and place. For more on this, see this question: Ending a letter in Latin. Nevertheless, there is also precedent for ending Latin letters in the way we are accustomed to.
A literal translation of your phrase is: humiliter tuus in Christo. I can't find any precedent for this, though, and I'm not sure if Latin shares this formula with English: it's strange for an adverb to modify a possessive pronoun.
I would suggest adding a noun, e.g. "servus" (=servant), for which I have found some precedent. You could thus close your letter with: humilis servus tuus in Christo [name]. This literally means, "Your humble servant in Christ." You could also substitute humillimus (="most humble").
The expression; "humilitate tua in Christo" means "with your humility in Christ", not quite what you have requested. A second problem is that "humilitas" is harsher, in Latin, than "humility" in English e.g. lowness; meanness; insignificance (Oxford).
A possible alternative: "minister tibi in Christo" = "a servant to you in Christ".
Here, "minister" is not so obsequious or humiliating as "humilitas"; besides "servant", "minister" = attendant; accomplice; agent.
Lewis & Short give more examples e.g. promoter; helper; an abettor; accomplice.
There was a greeting to a noble men in the former Austria-Hungary Empire: sounded like 'servus humillimus' (now clipped just to a 'servus' in some languages, which natives were citizens of the empire). Maybe it's possible to re-phrase expression in such way. Not adverb, but compound to modify pronoun. It sounds less pejoratively.