The options are very wide. You are not telling us what kind of cake you have in mind, so I'll be making a few assumptions here. But once you start thinking outside the box that equals "birthday cake" with "cake with different colours of icing", a whole world of options opens up.

1. Birthday cakes need not be (multi-)coloured.
   A one-tone cake that plays with texture can be very elegant, from luscious glossy chocolate ganache to swirls of light and fluffy frosting. You don't even need great piping skills (although it's a neat thing to master some day), heaping on the frosting and texturing into big fluffy "clouds" either with a spoon or a knife can be very beautiful and even my 7yo can produce very impressive results.

2. Find edible decorations for that pop of colour.
   A bright red strawberry or raspberry on a white frosting, a few sprigs of mint or chopped pistachios for a touch of green. Some lemon or orange zest, perhaps. Even some jam or a fruit compote will do, put on top or served as a sauce on the side. Or go for a nature walk and find edible flowers.

3. Choose non-edible decorations.
   Birthday candles aren't edible, so you can add more non-edible elements. Little flags on toothpicks or even a small garland held up by two or three large skewers come to mind. Perhaps spell out "HAPPY BIRTHDAY DAD" on bunting? Print a photo of your dad and mount it on a skewer or two? I have in the past even used toy figurines as cake topper. As long as everything that actually touches the cake is food safe, you needn't worry. You can use some parchment or plastic wrap to create a barrier under a topper, if necessary. The flags in the picture below are made from origami paper, masking tape is very handy, too, because it needs no extra glue.

Since it's last-minute, I'm guessing it'll be tough to work out natural colorings, so I'd avoid doing color-based decorations altogether.

You can use chocolate chips or shavings, nuts, fruit (fresh or dried), crumbled cookies, or anything else you like as toppings. I think even just an even coating of chopped nuts looks pretty good, but you can get pretty fancy with patterns, especially if you use more than one thing.

Or if you want something you can pipe on, make frosting and a ganache (or another frosting) in different colors - plain white and chocolate, or caramel, or maybe even fruit if you have something strongly colored you can puree.

What you are seeking are natural food dyes (or natural food colorings).

These are commercially available and you may find them at a local health or natural foods store or even a quality grocers.

They can be homemade, if you have the time and can get the ingredients.

Examples of their effects in buttercream:

(from Nourishing Joy)

Be careful not to end up with natural fabric dyes without careful checking, as many of these are toxic or bad tasting.

Takes very little turmeric to give a bright yellow colour - not enough to have a noticeable taste, especially if you use flavouring. Got any beets around? They give a lovely magenta red colour to food. Diluting would give a pale pink. Mashing fresh peppermint leaves will give a green juice but since you couldn't use much without thinning down the icing, it would likely be a pale green. I know of nothing that gives a blue colour since even blueberries cook a purple-red.

So forgoing blue, you can play around with those three shades to make some varied colours. None of this is helpful though if you don't have these ingredients. Hopefully, someone else may know of others.

Suggestions:

• Using a stencil, a seive and some icing sugar, you can create simple decorations known as cake dusting
  
• Consider using chocolate icing
• Fruit can be arranged on top to make wonderful toppings/decorations
  
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Jam or Jelly

Got a jar of jam or jelly in the fridge or pantry?

For jam, you may want to run through a sieve to remove seeds. You may need to add a bit of water or liquor to thin it out enough to press through. If too thin, simmer briefly on stove to evaporate.

Mix well to your batter or frosting for a bit of color.

Or swirl. After apportioning batter to the baking pans, plop some jelly and swirl with toothpicks or a thin knife.

Ditto for frosting, but you may want to practice first on a plate or waxed paper. If too thick for the frosting, thin a bit with water, liquor, or real maple syrup. Heating in a pan briefly can also help to thin.

Another alternative: Drizzle a series of lines across the top of the cake, then swipe across the lines with a toothpick to get the fancy effect seen commonly on Napoleon pastries. As seen here or seen here.

To prepare cake at last minute, i would make vanilla or chocolate flavoured pancakes or red velvet pancakes. For red color, I would use color from beet. Just grate and squeeze color from it and use how much you need.

Layer the pancakes by adding some whipped cream or chocolate ganache or cream cheese frosting which goes so well with red velvet pancake.

Top it with some more frosting and fruits of your choice. You can definitely play with flavours and look of it.