I had a beer with my supper and started to feel pretty good.
The beer I had with my dinner made me feel slightly intoxicated, but I feel good.
ーI had a beer with my supper and started to feel pretty good.
「夕食にビールを飲んで結構いい気分になってます」
to have a beer with one's supper で「夕食にビールを飲む」
to feel good で「気分が良い」
この言い方でほろ酔いなニュアンスも伝わりますよ。
ーThe beer I had with my dinner made me feel slightly intoxicated, but I feel good.
「夕飯に飲んだビールでほろ酔いだけどいい気分です」
to feel slightly intoxicated で「わずかに酔う感じがする」＝「ほろ酔い気分です」
ご参考まで！
I had a beer with dinner earlier, and now I'm feeling pleasantly buzzed.
「さっき夕食にビールを飲んで」は「I had a beer with dinner earlier」と表現します。「had」は「飲んだ」、「earlier」は「先ほど」を指します。
「ほろ酔いでいい気分です」は「I'm feeling pleasantly buzzed」と訳せます。「pleasantly」は「心地よく」、「buzzed」は「ほろ酔い」の状態を意味します。
カナダ 
アメリカ合衆国 
