Were any of the early church leaders Gentile converts to Christianity? By early, I mean the second half of the first century to the end of the second century.  I know, for example, that Paul and Barnabus were ethnic Jews.  The Apostle Paul mentions various Christians, such as Tychicus (a Greek name, meaning 'fortunate'), who came from Asia Minor (Colossians 4:7, 16; Ephesians 6:21–22; 2 Timothy 4:12; Titus 3:12).Source: Who was Tychicus?  

But was he a Jew, or was he a Gentile who converted to Christianity?

Later, we have Polycarp of Smyrna (died c. A.D. 155), Linus, and Clement of Rome (died c. A.D. 99), who are attributed as being bishops within the early Christian church. We also have Ignatius of Antioch (died c. A.D. 110).  But were they Jews or were they Gentile converts to Christianity?

Is there any information on the earliest recorded Gentiles who became leaders in the Christian church?
This question already has a lot of answers, but I feel like the most basic answer is missing!
The answer is yes, and we need look no further than the Bible.
Titus himself was a gentile convert. We learn this in Galatians 2

Galatians 2:3 nkjv - Yet not even Titus who was with me, being a Greek, was compelled to be circumcised.

For the sake of being concise, I wont quote more of the chapter, but you should check it out.
Now that we have established Titus Gentile-ness, we must ask the second question, was he a &quot;Leader in the early Church&quot;?
If we go to the book of Titus, we can find that out

Titus 1:5 nkjv - For this reason I left you in Crete, that you should set in order the things that are lacking, and appoint elders in every city as I commanded you
Titus 2:15 nkjv -  Speak these things, exhort, and rebuke with all authority. Let no one despise you.

So his job is to choose elders, teach , exhort, and rebuke, and in general get the churches in line. To me it is clear that Paul is asking Titus to act as a leader in the church.
Its at this point that the discussion gets more complicated if we don't have a shared doctrine of what constitutes an Elder/leader in the church etc, but personally I think this single example answers the original question quite nicely!