I recommend making two balls of white, and two of blue, this means for each diagonal stripe you aren't trailing wool on the wrong side. It will still get quite tangled if you aren't careful, but as it's only 22 rows of colour changing you should manage it if you do get a bit of a tangle.
Cast on 45 in red
row 1 - K21, sl1, K2TOG, PSSO, K21
row 2 and all even rows - knit all
row 3 - K20, sl1, K2TOG, PSSO, K20
row 5 - K19, sl1, K2TOG, PSSO, K19
row 7 - K18, sl1, K2TOG, PSSO, K18
row 9 - change to white wool; K17, sl1, K2TOG, PSSO, K17
row 11 - K16, sl1, K2TOG, PSSO, K16
row 13 - K11 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K11 blue
row 14 - K11 blue, K3 white, K3 red, K3 white, K11 blue
row 15 - K10 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K10 blue
row 16 - K10 blue, K3 white, K3 red, K3 white, K10 blue
row 17 - K9 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K9 blue
row 18 - K9 blue, K3 white, K3 red, K3 white, K9 blue
row 19 - K8 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K8 blue
row 20 - K8 blue, K3 white, K3 red, K3 white, K8 blue
row 21 - K7 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K7 blue
row 22 - K7 blue, K3 white, K3 red, K3 white, K7 blue
row 23 - K6 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K6 blue
row 24 - K6 blue, K3 white, K3 red, K3 white, K6 blue
row 25 - K5 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K5 blue
row 26 - K5 blue, K3 white, K3 red, K3 white, K5 blue
row 27 - K4 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K4 blue
row 28 - K4 blue, K3 white, K3 red, K3 white, K4 blue
row 29 - K3 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K3 blue
row 30 - K3 blue, K3 white, K3 red, K3 white, K3 blue
row 31 - K2 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K2 blue
row 32 - K2 blue, K3 white, K3 red, K3 white, K2 blue
row 33 - K1 blue, K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white, K1 blue
row 34 - K1 blue, K3 white, K3 red, K3 white, K1 blue
row 35 - K3 white, K1, sl1, K2TOG, PSSO, K1 red, K3 white
row 36 - K3 white, K3 red, K3 white
row 37 - K2 white, K1, sl1, K2TOG, PSSO, K1 red, K2 white
row 38 - K2 white, K3 red, K2 white
row 39 - K1 white, K1, sl1, K2TOG, PSSO, K1 red, K1 white
row 40 - K1 white, K3 red, K1 white
row 41 - K1, sl1, K2TOG, PSSO, K1 red,
row 42 - K3 red
row 43 - sl1, K2TOG, PSSO red
Thread yarn through remaining stitch, and weave in the ends.
And presto, a retro coaster promto!