If you're looking for pink, here's a shop that repairs and refinishes them (repaints) in pink: https://karlbusinessmachines.com/pink-typewriters/
As for natural pink manufactured typewriters, you're probably primarily looking at the Royal Quiet De Luxe (circa '55-58), Royal Futura 800, Royal FP (a larger heavy, standard desktop machine), the late 50's Smith-Corona 5 series (Clippers, Sterlings, Silent Supers). There were a few later in the 60s and 70s, but they're more difficult to find in the US and aren't as solid. These aren't rare typewriters, but generally because the collector's market likes color, you should expect to pay a $50-150 premium for pink in most online markets. Professional shops are much less likely to charge this sort of premium on pink unless it's for a machine they've had to strip down and repaint. (See also: https://www.reddit.com/r/typewriters/comments/1kw5jxh/what_are_your_thoughts_on_these_and_the_prices/)
For colloquial experience from a typewriter hunter from the Los Angeles area, I'll say I've been looking for a Cameo Pink smooth Royal FP for over a year and finally found one in solid, but restorable shape for $35, but it's taken a year of searching and it'll take a half-day's labor and some parts to clean it up to what a professional shop would consider solid working condition. In that time I've seen maybe half a dozen in online shops sell them in similar rough condition going for anywhere between $100 and $300. For your budget range, getting one from a professional shop is really the best, most economical way to go.
Please note that you positively don't want any of the new pink plastic typewriters made by "Royal Classic" or "We R Memory Keepers" (etc.) which you'll find on Amazon, Michaels, Home Depot, etc. for $200-300. They are dreadful machines, and if you really want one, save the money and buy one from ShopGoodwill.com for $5-15 instead.
If you wanted to go custom in your particular budget range, you might check out Gerren's work at Hot Rod Typewriter Co. where he does some truly gorgeous paint jobs on excellent typewriters. I suspect a pink Olympia SM3 from him would be a thing to behold.
Reply to u/dtja1l at https://old.reddit.com/r/typewriters/comments/1l0l6pi/help_finding_a_thoughtful_typewriter_as_a_gift/ with regard to buying a pink typewriter for a birthday present