We skip in Romans from Romans 2 to Romans 10 to find the next use of
“gospel.”  There are two uses of “gospel/gospeling” in Romans 10:15-16
and I have provided additional verses to exhibit the context:

8 … the word of faith we are proclaiming: 9 That if you confess with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. 10 For it is with your heart that you believe and are justified, and it is with your mouth that you confess and are saved.11 As the Scripture says, “Anyone who trusts in him will never be put to shame.” 12 For there is no difference between Jew and Gentile-the same Lord is Lord of all and richly blesses all who call on him, 13 for, “Everyone who calls on the name of the Lord will be saved.” 14 How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them? 15 And how can they preach unless they are sent? As it is written, “How beautiful are the feet of those who bring good news!” 16 But not all the Israelites accepted the good news. For Isaiah says, “Lord, who has believed our message?” 17 Consequently, faith comes from hearing the message, and the message is heard through the word of Christ. 18 But I ask: Did they not hear? Of course they did: “Their voice has gone out into all the earth, their words to the ends of the world.”

Observations about gospel here:

1.    The confession to gospel preaching is “Jesus is Lord.”
2.    This confession emerges from believing in the heart that God raised Jesus from the dead – resurrection is part of gospel preaching.
3.    Anyone – Jew or Gentile – can make this confession.
4.    These confessions follow from gospel preaching – and those charged with gospel preaching have “beautiful feet” or, better yet, “timely” feet or “opportune” feet.
5.    The gospel preaching here is preaching “good things.” [The Greek text says “gospeling good things.”] The gospel is good news.
6.    The elect people, Israel, did not all respond to the gospel preaching that called for the confession of Jesus as Lord.