Dinah said it! That's exactly right.
I think that Trip was always Archer's best friend, Trip was Malcolm's best friend, and Trip was T'Pol's best friend. While Malcolm was Trip's best guy friend and T'Pol was his best female friend (obviously).
In my E-squared when Trip dies, at the eulogy, Malcolm notices that many people had considered Trip their best friend. He says, Some people are just like that. In my story, Archer, Malcolm, T'Pol, Phlox, and Travis thought of Trip as their best friend. While Trip had considered Malcolm his best friend.
I think Trip and Archer had been best friends, but it's hard to stay best friends with your boss. So that definately got in the way of being buddies. Still they continued to love each other, more from a distance. As for friendship scenes between Trip and Archer, there was the delicious "Dessert Crossing." I think that episode summed up the dynamic. Archer begs Trip to go on that trip, Trip is grousing about it, recalling some earlier trip they took together that went array. He gives Archer some good advice when the bombs start dropping. I remember that scene when I write my Trip/Archer interactions. Trip accepts a subordinate role in relation to Archer but also has alot of confidence that his opinions matters to Archer. In Shuttlepod One, Trip recounts some scubadiving story, which shows he almost idolized Archer. You will recall that they were partners in crime during "First Flight" stealing the NX-01 prototype (off the top of my head). Trip pokes fun of Archer in episode where he goes to meet a Klingon woman and Trip tells Archer, like, "I've heard if they sense weakness they'll kill you. Go get 'em."
Actually, I enjoyed the complicated relationship after cogenitor. I loved the striken look on Trip's face when Archer would shout some order at him in a moment of heightened emotion. (For instance in The Chosen Realm, when Archer announces to Trip, they will cooperate with the Triannons.) I think the sharp tone directed at Trip meant: "No, Trip, you CAN'T sway me THIS time. (Even if we are friends and I know what you'd like to say about this.)" I think Trip was close enouph to the Captain that he always had a really good chance of swaying him if that was going to happen.
Finally, there were two episodes that showed how much Archer loved Trip even as he tries to stay professional. In "Observer Effect," there is a heartbreaking scene where Archer orders Trip to take some pills that will sedate him (so he won't get delerious and try to escape from quarantine. Trip doesn't want to take the pills and says, "But I might not wake up." Archer says somewhat firmly. "Trip, take the pills." Later when an Organian posing as Travis asks Archer if he would have begged the Klingons for an antidote, Archer says "On bended knee." In that scene you see how much Trip means to Archer. Also, the one great moment in the abomination is when Archer places Trip on the biobed and assures him everything will be fine and as soon as Trip disappears into the imaging chamber, Archer and Phlox exchange this stricken look of horror. Archer had to keep up a front of professionalism and neutrality, but he clearly loved Trip.